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Precalculus: Graphs and Models, A Right Triangle Approach

Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen

Chapter 8

Applications of Trigonometry - all with Video Answers

Educators

Section 1

The Law of Sines

08:18

Problem 1

Solve the triangle, if possible.
FIGURE CANT COPY

AG
Ankit Gupta
Numerade Educator
08:18

Problem 2

Solve the triangle, if possible.
FIGURE CANT COPY

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Ankit Gupta
Numerade Educator
08:18

Problem 3

Solve the triangle, if possible.
FIGURE CANT COPY

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Ankit Gupta
Numerade Educator
08:18

Problem 4

Solve the triangle, if possible.
FIGURE CANT COPY

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Ankit Gupta
Numerade Educator
04:43

Problem 5

Solve the triangle, if possible.
$$C=61^{\circ} 10^{\prime}, \quad c=30.3, b=24.2$$

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Ankit Gupta
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03:34

Problem 6

Solve the triangle, if possible.
$$A=126.5^{\circ}, a=17.2, c=13.5$$

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Ankit Gupta
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04:02

Problem 7

Solve the triangle, if possible.
$$c=3 \mathrm{mi}, B=37.48^{\circ}, C=32.16^{\circ}$$

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Ankit Gupta
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04:04

Problem 8

Solve the triangle, if possible.
$$a=2345 \mathrm{mi}, b=2345 \mathrm{mi}, A=124.67^{\circ}$$

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Ankit Gupta
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03:02

Problem 9

Solve the triangle, if possible.
$$b=56.78 \mathrm{yd}, c=56.78 \mathrm{yd}, C=83.78^{\circ}$$

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Ankit Gupta
Numerade Educator
03:06

Problem 10

Solve the triangle, if possible.
$$A=129^{\circ} 32^{\prime}, C=18^{\circ} 28^{\prime}, b=1204 \mathrm{in.}$$

AG
Ankit Gupta
Numerade Educator
03:43

Problem 11

Solve the triangle, if possible.
$$a=20.01 \mathrm{cm}, b=10.07 \mathrm{cm}, A=30.3^{\circ}$$

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Ankit Gupta
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04:17

Problem 12

Solve the triangle, if possible.
$$b=4.157 \mathrm{km}, c=3.446 \mathrm{km}, C=51^{\circ} 48^{\prime}$$

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Ankit Gupta
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02:00

Problem 13

Solve the triangle, if possible.
$$A=89^{\circ}, a=15.6 \text { in. }, b=18.4 \mathrm{in.}$$

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Ankit Gupta
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03:00

Problem 14

Solve the triangle, if possible.
$$C=46^{\circ} 32^{\prime}, a=56.2 \mathrm{m}, c=22.1 \mathrm{m}$$

AG
Ankit Gupta
Numerade Educator
03:45

Problem 15

Solve the triangle, if possible.
$$a=200 \mathrm{m}, A=32.76^{\circ}, C=21.97^{\circ}$$

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Ankit Gupta
Numerade Educator
02:18

Problem 16

Solve the triangle, if possible.
$$B=115^{\circ}, c=45.6 \mathrm{yd}, b=23.8 \mathrm{yd}$$

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Ankit Gupta
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00:50

Problem 17

Find the area of the triangle.
$$B=42^{\circ}, a=7.2 \mathrm{ft}, c=3.4 \mathrm{ft}$$

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Ankit Gupta
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01:07

Problem 18

Find the area of the triangle.
$$A=17^{\circ} 12^{\prime}, b=10 \text { in., } c=13 \text { in. }$$

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Ankit Gupta
Numerade Educator
01:00

Problem 19

Find the area of the triangle.
$$C=82^{\circ} 54^{\circ}, \quad a=4 \text { yd }, b=6 \text { yd }$$

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Ankit Gupta
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00:54

Problem 20

Find the area of the triangle.
$$C=75.16^{\circ}, a=1.5 \mathrm{m}, b=2.1 \mathrm{m}$$

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Ankit Gupta
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01:14

Problem 21

Find the area of the triangle.
$$B=135.2^{\circ}, a=46.12 \mathrm{ft}, c=36.74 \mathrm{ft}$$

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Ankit Gupta
Numerade Educator
00:48

Problem 22

Find the area of the triangle.
$$A=113^{\circ}, b=18.2 \mathrm{cm}, c=23.7 \mathrm{cm}$$

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Ankit Gupta
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02:11

Problem 23

Lawn Irrigation. Sanchez Irrigation is installing a lawn irrigation system with three heads. They determine that the best locations for the heads $A, B,$ and $C$ are such that $\angle C A B$ is $40^{\circ}$ and $\angle A C B$ is $45^{\circ}$ and that the distance from $A$ to $B$ is 34 ft. Find the distance from $B$ to $C$
GRAPH CANT COPY

Khushbu Rani
Khushbu Rani
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03:47

Problem 24

Meteor Crater The Meteor Crater in northern Arizona is the earliest discovered meteorite impact crater. A math student locates points $R$ and $S$ on opposite sides of the crater and point $T 700$ ft from $S .$ The measures of $\angle R S T$ and $\angle R T S$ are estimated to be $95^{\circ}$ and $75^{\circ},$ respectively. What is the width of the crater from point $R$ to point $S ?$
PICTURE CANT COPY

Allison Knapp
Allison Knapp
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01:24

Problem 25

A new homeowner has a triangular-shaped back yard. Two of the three sides measure $53 \mathrm{ft}$ and $42 \mathrm{ft}$ and form an included angle of $135^{\circ} .$ To determine the amount of fertilizer and grass seed to be purchased, the owner must know, or at least approximate, the area of the yard. Find the area of the yard to the nearest square foot.

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Ankit Gupta
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04:18

Problem 26

A zoo is expanding its African elephant exhibit and needs to fence an outdoor triangular area, with a barn forming one side of the triangle. The maintenance department has only 168 ft of fencing in stock. If one side of the outdoor area is $92 \mathrm{ft}$ and the angle that it makes with the barn is $78^{\circ}$ does the zoo need to order more fencing?
PICTURE CANT COPY

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Ankit Gupta
Numerade Educator
01:13

Problem 27

A pole leans away from the sun at an angle of $7^{\circ}$ to the vertical. When the angle of elevation of the sun is $51^{\circ},$ the pole casts a shadow $47 \mathrm{ft}$ long on level ground. How long is the pole?
PICTURE CANT COPY

Erika Bustos
Erika Bustos
Numerade Educator
04:47

Problem 28

Keep in mind the two types of bearing considered in Sections 6.2 and 6.3
A reconnaissance airplane leaves its airport on the east coast of the United States and flies in a direction of $85^{\circ} .$ Because of bad weather, it returns to another airport $230 \mathrm{km}$ due north of its home base. To get to the new airport, it flies in a direction of $283^{\circ} .$ What is the total distance that the airplane flew?
GRAPH CANT COPY

Sheryl Ezze
Sheryl Ezze
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04:23

Problem 29

Keep in mind the two types of bearing considered in Sections 6.2 and 6.3
A ranger in fire tower $A$ spots a fire at a direction of $295^{\circ} .$ A ranger in fire tower $B,$ located $45 \mathrm{mi}$ at a direction of $45^{\circ}$ from tower $A,$ spots the same fire at a direction of $255^{\circ} .$ How far from tower $A$ is the fire? from tower $B ?$
GRAPH CANT COPY

AG
Ankit Gupta
Numerade Educator
04:54

Problem 30

Keep in mind the two types of bearing considered in Sections 6.2 and 6.3
A boat leaves lighthouse $A$ and sails
$5.1 \mathrm{km} .$ At this time is is sighted from lighthouse $B$
7.2 $\mathrm{km}$ west of $A$. The bearing of the boat from $B$ is $\mathrm{N} 65^{\circ} 10^{\prime} \mathrm{E} .$ How far is the boat from $B ?$
PICTURE CANT COPY

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Ankit Gupta
Numerade Educator
05:11

Problem 31

Keep in mind the two types of bearing considered in Sections 6.2 and 6.3
Miami, Florida, is located $178 \mathrm{mi} \mathrm{N} 73^{\circ} 10^{\prime} \mathrm{W}$ of Nassau. Because of an approaching hurricane, a cruise ship sailing in the region needs to know how far it is from Nassau. The ship's position is N77' 43'E of Miami and N19 $^{\circ} 35^{\prime} \mathrm{E}$ of Nassau. How far is the ship from Nassau?
PICTURE CANT COPY

AG
Ankit Gupta
Numerade Educator
02:15

Problem 32

Three gears are arranged as shown in the following figure. Find the angle $\phi$
GRAPH CANT COPY

Erika Bustos
Erika Bustos
Numerade Educator
00:43

Problem 33

Find the acute angle $A,$ in both radians and degrees, for the given function value. [ 6.1]
$$\cos A=0.2213$$

Erika Bustos
Erika Bustos
Numerade Educator
00:45

Problem 34

Find the acute angle $A,$ in both radians and degrees, for the given function value. [ 6.1]
$$\cos A=1.5612$$

Erika Bustos
Erika Bustos
Numerade Educator
01:38

Problem 35

Convert to decimal degree notation. Round to the nearest hundredth.
$$18^{\circ} 14^{\prime} 20^{\prime \prime}$$

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Ankit Gupta
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01:11

Problem 36

Convert to decimal degree notation. Round to the nearest hundredth.
$$125^{\circ} 3^{\prime} 42^{\prime \prime}$$

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Ankit Gupta
Numerade Educator
00:17

Problem 37

$$\text { Given that } f(x)=\sqrt{x-6}, \text { find } f(31)$$

Erika Bustos
Erika Bustos
Numerade Educator
00:33

Problem 38

Find the value.
$$\cos \frac{\pi}{6}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:29

Problem 39

Find the value.
$$\sin 45^{\circ}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:27

Problem 40

Find the value.
$$\sin 300^{\circ}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:38

Problem 41

Find the value.
$$\cos \left(-\frac{2 \pi}{3}\right)$$

Erika Bustos
Erika Bustos
Numerade Educator
00:28

Problem 42

Multiply: $(1-i)(1+i)$

Erika Bustos
Erika Bustos
Numerade Educator
02:48

Problem 43

Prove the following area formulas for a general triangle $A B C$ with area represented by $K$
$$\begin{array}{l}K=\frac{a^{2} \sin B \sin C}{2 \sin A}, \quad K=\frac{c^{2} \sin A \sin B}{2 \sin C} \\K=\frac{b^{2} \sin C \sin A}{2 \sin B}\end{array}$$

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Ankit Gupta
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02:08

Problem 44

Prove that the area of a parallelogram is the product of two adjacent sides and the sine of the included angle.
GRAPH CANT COPY

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Ankit Gupta
Numerade Educator
02:08

Problem 45

Prove that the area of a quadrilateral $A B C D$ is one-half of the product of the lengths of its diagonals and the sine of the angle $\theta$ between the diagonals.
GRAPH CANT COPY

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Ankit Gupta
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01:22

Problem 46

Find $d$
GRAPH CANT COPY

Trinity Steen
Trinity Steen
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05:58

Problem 47

A musician is constructing an octagonal recording studio in his home. The studio with dimensions as shown below is to be built within a rectangular $31^{\prime} 9^{\prime \prime}$ by $29^{\prime} 9^{\prime \prime}$ room (Source: Tony Medeiros, Indianapolis, IN). Point $D$ is $9^{\prime \prime}$ from wall 2 , and points $C$ and $B$ are each $9^{\prime \prime}$ from wall $1 .$ Using the law of sines and right triangles, determine to the nearest tenth of an inch how far point $A$ is from wall 1 and from wall 4. (For more information on this studio, see Example 2 in Section $8.2 .$ )
GRAPH CANT COPY

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Ankit Gupta
Numerade Educator