Precalculus Student Solutions Manual 5th

Margaret L. Lial, John Hornsby, David I. Schneider

Chapter 6

The Circular Functions and Their Graphs - all with Video Answers

Educators

Section 1

Radian Measure

Problem 1

Give the radian measure of the angle. (It helps to remember that $\pi \approx 3 .)$
(FIGURE CANNOT COPY)

Amy Jiang

Amy Jiang

Numerade Educator

Problem 2

Give the radian measure of the angle. (It helps to remember that $\pi \approx 3 .)$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 3

Give the radian measure of the angle. (It helps to remember that $\pi \approx 3 .)$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 4

Give the radian measure of the angle. (It helps to remember that $\pi \approx 3 .)$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 5

Give the radian measure of the angle. (It helps to remember that $\pi \approx 3 .)$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 6

Give the radian measure of the angle. (It helps to remember that $\pi \approx 3 .)$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 7

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$60^{\circ}$$

Amy Jiang

Numerade Educator

Problem 8

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$30^{\circ}$$

Amy Jiang

Numerade Educator

Problem 9

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$90^{\circ}$$

Amy Jiang

Numerade Educator

Problem 10

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$120^{\circ}$$

Amy Jiang

Numerade Educator

Problem 11

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$150^{\circ}$$

Amy Jiang

Numerade Educator

Problem 12

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$270^{\circ}$$

Amy Jiang

Numerade Educator

Problem 13

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$-300^{\circ}$$

Amy Jiang

Numerade Educator

Problem 14

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$-315^{\circ}$$

Amy Jiang

Numerade Educator

Problem 15

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$450^{\circ}$$

Amy Jiang

Numerade Educator

Problem 16

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$480^{\circ}$$

Amy Jiang

Numerade Educator

Problem 17

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$1800^{\circ}$$

Amy Jiang

Numerade Educator

Problem 18

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$3600^{\circ}$$

Amy Jiang

Numerade Educator

Problem 19

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$0^{\circ}$$

Amy Jiang

Numerade Educator

Problem 20

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$180^{\circ}$$

Amy Jiang

Numerade Educator

Problem 21

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$-900^{\circ}$$

Amy Jiang

Numerade Educator

Problem 22

Convert each degree measure to radians. Leave answers as multiples of $\pi .$
$$-1800^{\circ}$$

Amy Jiang

Numerade Educator

Problem 23

Give a short explanation
Explain how to convert degree measure to radian measure.

Amy Jiang

Numerade Educator

Problem 24

Give a short explanation
Explain how to convert radian measure to degree measure.

Amy Jiang

Numerade Educator

Problem 25

Give a short explanation
Explain the meaning of radian measure.

Amy Jiang

Numerade Educator

Problem 26

Give a short explanation
Explain the difference between degree measure and radian measure.

Amy Jiang

Numerade Educator

Problem 27

Give a short explanation
Use an example to show that you can convert from radian measure to degree measure by multiplying by $\frac{180^{\circ}}{\pi}$

Amy Jiang

Numerade Educator

Problem 28

Give a short explanation
Explain why an angle of radian measure $t$ in standard position intercepts an arc of length $t$ on a circle of radius 1

Amy Jiang

Numerade Educator

Problem 29

Convert each radian measure to degrees.
$$\frac{\pi}{3}$$

Amy Jiang

Numerade Educator

Problem 30

Convert each radian measure to degrees.
$$\frac{8 \pi}{3}$$

Amy Jiang

Numerade Educator

Problem 31

Convert each radian measure to degrees.
$$\frac{7 \pi}{4}$$

Amy Jiang

Numerade Educator

Problem 32

Convert each radian measure to degrees.
$$\frac{2 \pi}{3}$$

Amy Jiang

Numerade Educator

Problem 33

Convert each radian measure to degrees.
$$\frac{11 \pi}{6}$$

Amy Jiang

Numerade Educator

Problem 34

Convert each radian measure to degrees.
$$\frac{15 \pi}{4}$$

Amy Jiang

Numerade Educator

Problem 35

Convert each radian measure to degrees.
$$\frac{\pi}{6}$$

Amy Jiang

Numerade Educator

Problem 36

Convert each radian measure to degrees.
$$-\frac{8 \pi}{5}$$

Amy Jiang

Numerade Educator

Problem 37

Convert each radian measure to degrees.
$$\frac{7 \pi}{10}$$

Amy Jiang

Numerade Educator

Problem 38

Convert each radian measure to degrees.
$$\frac{11 \pi}{15}$$

Amy Jiang

Numerade Educator

Problem 39

Convert each radian measure to degrees.
$$-\frac{4 \pi}{15}$$

Amy Jiang

Numerade Educator

Problem 40

Convert each radian measure to degrees.
$$-\frac{7 \pi}{20}$$

Amy Jiang

Numerade Educator

Problem 41

Convert each radian measure to degrees.
$$\frac{17 \pi}{20}$$

Amy Jiang

Numerade Educator

Problem 42

Convert each radian measure to degrees.
$$\frac{11 \pi}{30}$$

Amy Jiang

Numerade Educator

Problem 43

Convert each radian measure to degrees.
$$-5 \pi$$

Amy Jiang

Numerade Educator

Problem 44

Convert each radian measure to degrees.
$$15 \pi$$

Amy Jiang

Numerade Educator

Problem 45

Convert each degree measure to radians.
$$39^{\circ}$$

Amy Jiang

Numerade Educator

Problem 46

Convert each degree measure to radians.
$$74^{\circ}$$

Amy Jiang

Numerade Educator

Problem 47

Convert each degree measure to radians.
$$42.5^{\circ}$$

Amy Jiang

Numerade Educator

Problem 48

Convert each degree measure to radians.
$$264.9^{\circ}$$

Amy Jiang

Numerade Educator

Problem 49

Convert each degree measure to radians.
$$139^{\circ} 10^{\prime}$$

Amy Jiang

Numerade Educator

Problem 50

Convert each degree measure to radians.
$$174^{\circ} 50^{\prime}$$

Amy Jiang

Numerade Educator

Problem 51

Convert each degree measure to radians.
$$64.29^{\circ}$$

Amy Jiang

Numerade Educator

Problem 52

Convert each degree measure to radians.
$$85.04^{\circ}$$

Amy Jiang

Numerade Educator

Problem 53

Convert each degree measure to radians.
$$56^{\circ} 25^{\prime}$$

Amy Jiang

Numerade Educator

Problem 54

Convert each degree measure to radians.
$$122^{\circ} 37^{\prime}$$

Amy Jiang

Numerade Educator

Problem 55

Convert each degree measure to radians.
$$-47.6925^{\circ}$$

Amy Jiang

Numerade Educator

Problem 56

Convert each degree measure to radians.
$$-23.0143^{\circ}$$

Amy Jiang

Numerade Educator

Problem 57

Convert each radian measure to degrees. Write answers to the nearest minute.
$$2$$

Amy Jiang

Numerade Educator

Problem 58

Convert each radian measure to degrees. Write answers to the nearest minute.
$$5$$

Amy Jiang

Numerade Educator

Problem 59

Convert each radian measure to degrees. Write answers to the nearest minute.
$$1.74$$

Amy Jiang

Numerade Educator

Problem 60

Convert each radian measure to degrees. Write answers to the nearest minute.
$$3.06$$

Amy Jiang

Numerade Educator

Problem 61

Convert each radian measure to degrees. Write answers to the nearest minute.
$$0.3417$$

Amy Jiang

Numerade Educator

Problem 62

Convert each radian measure to degrees. Write answers to the nearest minute.
$$9.84763$$

Amy Jiang

Numerade Educator

Problem 63

Convert each radian measure to degrees. Write answers to the nearest minute.
$$-5.01095$$

Amy Jiang

Numerade Educator

Problem 64

Convert each radian measure to degrees. Write answers to the nearest minute.
$$-3.47189$$

Amy Jiang

Numerade Educator

Problem 65

The figure shows the same angles measured in both degrees and radians. Complete the missing measures.
(FIGURE CANNOT COPY)

Katelyn Chen

Numerade Educator

Problem 66

What would be the exact radian measure of an angle that measures $\pi$ degrees?

Amy Jiang

Numerade Educator

Problem 67

Find the exact length of each arc intercepted by the given central angle.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 68

Find the exact length of each arc intercepted by the given central angle.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 69

Find the exact length of each arc intercepted by the given central angle.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 70

Find the radius of each circle.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 71

Find the radius of each circle.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 72

Find the radius of each circle.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 73

Find the measure of each central angle (in radians).
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 74

Find the measure of each central angle (in radians).
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 75

Find the measure of each central angle (in radians).
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 76

Explain how to find the deg ree measure of a central angle in a circle if both the radius and the length of the intercepted arc are known.

Amy Jiang

Numerade Educator

Problem 77

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=12.3 \mathrm{cm}, \theta=\frac{2 \pi}{3} \mathrm{radians}$$

Amy Jiang

Numerade Educator

Problem 78

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=0.892 \mathrm{cm}, \theta=\frac{11 \pi}{10} \mathrm{radians}$$

Amy Jiang

Numerade Educator

Problem 79

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=1.38 \mathrm{ft}, \theta=\frac{5 \pi}{6} \mathrm{radians}$$

Amy Jiang

Numerade Educator

Problem 80

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=3.24 \mathrm{mi}, \theta=\frac{7 \pi}{6} \mathrm{radians}$$

Amy Jiang

Numerade Educator

Problem 81

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=4.82 \mathrm{m}, \quad \theta=60^{\circ}$$

Amy Jiang

Numerade Educator

Problem 82

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=71.9 \mathrm{cm}, \theta=135^{\circ}$$

Amy Jiang

Numerade Educator

Problem 83

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=15.1 \text { in., } \theta=210^{\circ}$$

Amy Jiang

Numerade Educator

Problem 84

Find the length to three significant digits of each arc intercepted by a central angle $\theta$ in a circle of radius $r$.
$$r=12.4 \mathrm{ft}, \theta=330^{\circ}$$

Amy Jiang

Numerade Educator

Problem 85

If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

Amy Jiang

Numerade Educator

Problem 86

Radian measure simplifies many formulas, such as the formula for arc length, $s=r \theta .$ Give the corresponding formula when $\theta$ is measured in degrees instead of radians.

Amy Jiang

Numerade Educator

Problem 87

Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Use $r=6400 \mathrm{km}$ for the radius of Earth.
Panama City, Panama, $9^{\circ} \mathrm{N},$ and Pittsburgh, Pennsylvania, $40^{\circ} \mathrm{N}$

Amy Jiang

Numerade Educator

Problem 88

Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Use $r=6400 \mathrm{km}$ for the radius of Earth.
Farmersville, California, $36^{\circ} \mathrm{N},$ and Penticton, British Columbia, $49^{\circ} \mathrm{N}$

Amy Jiang

Numerade Educator

Problem 89

Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Use $r=6400 \mathrm{km}$ for the radius of Earth.
New York City, New York, $41^{\circ} \mathrm{N},$ and Lima, Peru, $12^{\circ} \mathrm{S}$

Amy Jiang

Numerade Educator

Problem 90

Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Use $r=6400 \mathrm{km}$ for the radius of Earth.
Halifax, Nova Scotia, $45^{\circ} \mathrm{N},$ and Buenos Aires, Argentina, $34^{\circ} \mathrm{S}$

Amy Jiang

Numerade Educator

Problem 91

Madison, South Dakota, and Dallas, Texas, are $1200 \mathrm{km}$ apart and lie on the same north-south line. The latitude of Dallas is $33^{\circ} \mathrm{N}$. What is the latitude of Madison?

Amy Jiang

Numerade Educator

Problem 92

Charleston, South Carolina, and Toronto, Canada, are $1100 \mathrm{km}$ apart and lie on the same north-south line. The latitude of Charleston is $33^{\circ} \mathrm{N}$. What
is the latitude of Toronto?

Amy Jiang

Numerade Educator

Problem 93

Work each problem.
Two gears are adjusted so that the smaller gear drives the larger one, as shown in the figure. If the smaller gear rotates through an angle of $300^{\circ},$ through how many degrees does the larger gear rotate?

Harsh Gadhiya

Numerade Educator

Problem 94

Work each problem.
Repeat Exercise 93 for gear radii of 4.8 in. and 7.1 in. and for an angle of $315^{\circ}$ for the smaller gear.

Harsh Gadhiya

Numerade Educator

Problem 95

Work each problem.
The rotation of the smaller wheel in the figure causes the larger wheel to rotate. Through how many degrees does the larger wheel rotate if the smaller one rotates through $60.0^{\circ} ?$

Harsh Gadhiya

Numerade Educator

Problem 96

Work each problem.
Repeat Exercise 95 for wheel radii of 6.84 in. and 12.46 in. and an angle of $150^{\circ}$ for the smaller wheel.

Harsh Gadhiya

Numerade Educator

Problem 97

Work each problem.
Find the radius of the larger wheel in the figure if the smaller wheel rotates $80.0^{\circ}$ when the larger wheel rotates $50.0^{\circ}$

Harsh Gadhiya

Numerade Educator

Problem 98

Work each problem.
Repeat Exercise 97 if the smaller wheel of radius 14.6 in. rotates $120^{\circ}$ when the larger wheel rotates $60^{\circ} .$

Harsh Gadhiya

Numerade Educator

Problem 99

Work each problem.
Refer to the figure.
(a) How many inches will the weight in the figure rise if the pulley is rotated through an angle of $71^{\circ} 50^{\prime} ?$
(b) Through what angle, to the nearest minute, must the pulley be rotated to raise the weight 6 in.?

Aman Gupta

Numerade Educator

Problem 100

Work each problem.
Find the radius of the pulley in the figure if a rotation of $51.6^{\circ}$ raises the weight $11.4 \mathrm{cm} .$

Harsh Gadhiya

Numerade Educator

Problem 101

Bicycle Chain Drive The figure shows the chain drive of a bicycle. How far will the bicycle move if the pedals are rotated through $180^{\circ} ?$ Assume the radius of the bicycle wheel is 13.6 in.
(FIGURE CANNOT COPY)

MM

Milena Milkova

Numerade Educator

Problem 102

The speedometer of Terry's Honda CR-V is designed to be accurate with tires of radius 14 in.
(a) Find the number of rotations of a tire in 1 hr if the car is driven at 55 mph.
(b) Suppose that oversize tires of radius 16 in. are placed on the car. If the car is now driven for 1 hr with the speedometer reading 55 mph, how far has the car gone? If the speed limit is 55 mph, does Terry deserve a speeding ticket?

Abhishek Kumar

Numerade Educator

Problem 103

Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand.
30 min
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 104

Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand.
$$40 \mathrm{min}$$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 105

Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand.
$$4.5 \mathrm{hr}$$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 106

Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand.
$$6 \frac{1}{2} \mathrm{hr}$$
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 107

A railroad track in the desert is $3.5 \mathrm{km}$ away. A train on the track subtends (horizontally) an angle of $3^{\circ} 20^{\prime} .$ Find the length of the train.

Teresa Fuston

Numerade Educator

Problem 108

The mast of Brent Simon's boat is 32 ft high. If it subtends an angle of $2^{\circ} 10^{\prime},$ how far away is it?

Abigail Polmanteer

Abigail Polmanteer

Numerade Educator

Problem 109

Find the area of each sector.
(FIGURE CANNOT COPY)

Julian Wong

Numerade Educator

Problem 110

Find the area of each sector.
(FIGURE CANNOT COPY)

Julian Wong

Numerade Educator

Problem 111

Find the area of each sector.
(FIGURE CANNOT COPY)

Julian Wong

Numerade Educator

Problem 112

Find the area of each sector.
(FIGURE CANNOT COPY)

Julian Wong

Numerade Educator

Problem 113

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 114

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 115

Find the measure (in radians) of each central angle. The number inside the sector is the area.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 116

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
(FIGURE CANNOT COPY)

Amy Jiang

Numerade Educator

Problem 117

Find the area of a sector of a circle having radius $r$ and central angle $\theta .$ Express answers to the nearest tenth.
$$r=29.2 \mathrm{m}, \theta=\frac{5 \pi}{6} \mathrm{radians}$$

Amy Jiang

Numerade Educator

Problem 118

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
$$r=59.8 \mathrm{km}, \theta=\frac{2 \pi}{3} \mathrm{radians}$$

Amy Jiang

Numerade Educator

Problem 119

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
$$r=30.0 \mathrm{ft}, \theta=\frac{\pi}{2} \mathrm{radians}$$

Amy Jiang

Numerade Educator

Problem 120

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
$$r=90.0 \mathrm{yd}, \theta=\frac{5 \pi}{6} \text { radians }$$

Amy Jiang

Numerade Educator

Problem 121

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
$$r=12.7 \mathrm{cm}, \theta=81^{\circ}$$

Amy Jiang

Numerade Educator

Problem 122

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
$$r=18.3 \mathrm{m}, \theta=125^{\circ}$$

Amy Jiang

Numerade Educator

Problem 123

Find the measure (in degrees) of each central angle. The number inside the sector is the area.
$$r=40.0 \mathrm{mi}, \theta=135^{\circ}$$

Amy Jiang

Numerade Educator

Problem 124

Find the area of a sector of a circle having radius $r$ and central angle $\boldsymbol{\theta}$. Express answers to the nearest tenth.
$$r=90.0 \mathrm{km}, \theta=270^{\circ}$$

Amy Jiang

Numerade Educator

Problem 125

Work each problem.
Find the measure (in radians) of a central angle of a sector of area 16 in. $^{2}$ in a circle of radius 3.0 in.

Amy Jiang

Numerade Educator

Problem 126

Work each problem.
Find the radius of a circle in which a central angle of $\frac{\pi}{6}$ radian determines a sector of area $64 \mathrm{m}^{2}$

Amy Jiang

Numerade Educator

Problem 127

Work each problem.
A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if $\theta=40.0^{\circ}$ and $r=152$ yd.

Amy Jiang

Numerade Educator

Problem 128

Work each problem.
Suppose that in Exercise 127 the angle is halved and the radius length is doubled. How does the new area compare to the original area? Does this result hold in general for any values
of $\theta$ and $r ?$

Amy Jiang

Numerade Educator

Problem 129

Work each problem.
A circular sector has an area of 50 in.?. The radius of the circle is 5 in. What is the arc length of the sector?

Amy Jiang

Numerade Educator

Problem 130

Work each problem.
In a circle, a sector has an area of $16 \mathrm{cm}^{2}$ and an arc length of $6.0 \mathrm{cm}$. What is the measure of the central angle in degrees?

Aman Gupta

Numerade Educator

Problem 131

Work each problem.
The figure illustrates Medicine Wheel, a Native American structure in northern Wyoming. There are 27 aboriginal spokes in the wheel, all equally spaced.
(FIGURE CANNOT COPY)
(a) Find the measure of each central angle in degrees and in radians.
(b) If the radius of the wheel is $76.0 \mathrm{ft}$, find the circumference.
(c) Find the length of each arc intercepted by consecutive pairs of spokes.
(d) Find the area of each sector formed by consecutive spokes.

Aman Gupta

Numerade Educator

Problem 132

Wiper The Ford Model A, built from 1928 to $1931,$ had a single windshield wiper on the driver's side. The total arm and blade was 10 in. long and rotated back and forth through an angle of $95^{\circ} .$ The shaded region in the figure is the portion of the windshield cleaned by the 7 -in. wiper blade. What is the area of the region cleaned?
(FIGURE CANNOT COPY)

Harsh Gadhiya

Numerade Educator

Problem 133

In the United States, circular railroad curves are designated by the degree of curvature, the central angle subtended by a chord of 100 ft. Suppose a portion of track has curvature $42.0^{\circ} .$
(a) What is the radius of the curve?
(b) What is the length of the arc determined by the 100 -ft chord?
(c) What is the area of the portion of the circle bounded by the arc and the $100-\mathrm{ft}$ chord?

Sheryl Ezze

Numerade Educator

Problem 134

A 300 -megawatt solar-power plant requires approximately $950,000 \mathrm{m}^{2}$ of land area to collect the required amount of energy from sunlight. If this land area is circular, what is its radius? If this land area is a $35^{\circ}$ sector of a circle, what is its radius?

Anas Venkitta

Numerade Educator

Problem 135

A frequent problem in surveying city lots and rural lands adjacent to curves of highways and railways is that of finding the area when one or more of the boundary lines is the arc of a circle. Find the area (to two significant digits) of the lot shown in the figure.
(FIGURE CANNOT COPY)

Cullen Miller

Numerade Educator

Problem 136

Nautical miles are used by ships and airplanes. They are different from statute miles, which equal 5280 ft. A nautical mile is defined to be the arc length along the equator intercepted by a central angle $A O B$ of $1 \mathrm{min},$ as illustrated in the figure. If the equatorial radius of Earth is $3963 \mathrm{mi}$, use the arc length formula to approximate the number of statute miles in 1 nautical mile. Round your answer to two decimal places.
(FIGURE CANNOT COPY)

Harsh Gadhiya

Numerade Educator