Algebra 2 and Trigonometry

Ann Xavier Gantert

Chapter 14

TRIGONOMETRIC APPLICATIONS - all with Video Answers

Educators

JM

TO

Section 1

Similar Triangles

Problem 1

In Example $2,$ is it possible to find the measure of $\theta$ without first finding $O A ?$ Justify your answer.

Amy Jiang

Amy Jiang

Numerade Educator

Problem 2

In what quadrant is a point whose coordinates in radian measure are $\left(2 \cos \frac{4 \pi}{3}, 2 \sin \frac{4 \pi}{3}\right) ?$ Justify your answer.

Joshua Utley

Numerade Educator

Problem 3

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=4, \theta=45^{\circ}$

Joshua Utley

Numerade Educator

Problem 4

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=2, \theta=30^{\circ}$

Joshua Utley

Numerade Educator

Problem 5

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=6, \theta=90^{\circ}$

Joshua Utley

Numerade Educator

Problem 6

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=8, \theta=120^{\circ}$

Joshua Utley

Numerade Educator

Problem 7

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=15, \theta=135^{\circ}$

Joshua Utley

Numerade Educator

Problem 8

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=0.5, \theta=180^{\circ}$

Joshua Utley

Numerade Educator

Problem 9

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=9, \theta=150^{\circ}$

Joshua Utley

Numerade Educator

Problem 10

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=25, \theta=210^{\circ}$

Joshua Utley

Numerade Educator

Problem 11

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=12, \theta=270^{\circ}$

Joshua Utley

Numerade Educator

Problem 12

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=\sqrt{2}, \theta=225^{\circ}$

Joshua Utley

Numerade Educator

Problem 13

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=\sqrt{3}, \theta=300^{\circ}$

Joshua Utley

Numerade Educator

Problem 14

Write in simplest radical form the coordinates of each point $A$ if $A$ is on the terminal side of an angle in standard position whose degree measure is $\theta .$
$O A=2, \theta=-60^{\circ}$

Joshua Utley

Numerade Educator

Problem 15

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(6,8)$

Joshua Utley

Numerade Educator

Problem 16

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(-5,12)$

Joshua Utley

Numerade Educator

Problem 17

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(0,7)$

Ashley Graham

Numerade Educator

Problem 18

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(12,-9)$

Joshua Utley

Numerade Educator

Problem 19

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(15,0)$

Ashley Graham

Numerade Educator

Problem 20

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(-8,-12)$

Joshua Utley

Numerade Educator

Problem 21

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(24,7)$

Ashley Graham

Numerade Educator

Problem 22

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(6,-10)$

Joshua Utley

Numerade Educator

Problem 23

The coordinates of a point are given. a. Find the distance of the point from the origin. Express approximate distances to the nearest hundredth. b. Find the measure, to the nearest degree, of the angle in standard position whose terminal side contains the given point.
$(-8,8)$

Joshua Utley

Numerade Educator

Problem 24

For each $\triangle O R S, O$ is the origin, $R$ is on the positive ray of the $x$ -axis and $\overline{P S}$ is the altitude from $S$ to $\overrightarrow{O R}$ . Find the exact coordinates of $R$ and $S .$ b. Find the exact area of $\triangle O R S .$
$O R=5, \mathrm{m} \angle R O S=\frac{\pi}{3}, O S=3$

Joshua Utley

Numerade Educator

Problem 25

For each $\triangle O R S, O$ is the origin, $R$ is on the positive ray of the $x$ -axis and $\overline{P S}$ is the altitude from $S$ to $\overrightarrow{O R}$ . Find the exact coordinates of $R$ and $S .$ b. Find the exact area of $\triangle O R S .$
$O R=12, \mathrm{m} \angle R O S=\frac{\pi}{2}, O S=8$

JM

John Martin

Numerade Educator

Problem 26

For each $\triangle O R S, O$ is the origin, $R$ is on the positive ray of the $x$ -axis and $\overline{P S}$ is the altitude from $S$ to $\overrightarrow{O R}$ . Find the exact coordinates of $R$ and $S .$ b. Find the exact area of $\triangle O R S .$
$O R=8, \mathrm{m} \angle R O S=\frac{3 \pi}{4}, O S=8$

Joshua Utley

Numerade Educator

Problem 27

For each $\triangle O R S, O$ is the origin, $R$ is on the positive ray of the $x$ -axis and $\overline{P S}$ is the altitude from $S$ to $\overrightarrow{O R}$ . Find the exact coordinates of $R$ and $S .$ b. Find the exact area of $\triangle O R S .$
$O R=20, O S=R S, P S=10$

JM

John Martin

Numerade Educator

Problem 28

For each $\triangle O R S, O$ is the origin, $R$ is on the positive ray of the $x$ -axis and $\overline{P S}$ is the altitude from $S$ to $\overrightarrow{O R}$ . Find the exact coordinates of $R$ and $S .$ b. Find the exact area of $\triangle O R S .$
$O R=9, \triangle O R S$ is equilateral

Joshua Utley

Numerade Educator

Problem 29

For each $\triangle O R S, O$ is the origin, $R$ is on the positive ray of the $x$ -axis and $\overline{P S}$ is the altitude from $S$ to $\overrightarrow{O R}$ . Find the exact coordinates of $R$ and $S .$ b. Find the exact area of $\triangle O R S .$
$O R=7, \mathrm{m} \angle R O S=\frac{\pi}{6}, P S=8$

JM

John Martin

Numerade Educator