Deck 7: Trigonometry in Circles and Triangles

Question 1

Find the area of the following triangle if a = 11, b = 8, and A = 85 . Round to two decimal places.

Answer 1

32.99

Question 2

Find the area of a triangle with angles if the length of the side opposite the angle is 8. Round to 2 decimal places.

Answer 2

10.97

Question 3

Two airplanes are headed toward the same airport. The first plane is flying 168 mph and the second plane is flying 135 mph. The angle between the planes with its vertex at the airport is . If both planes reach the airport in 2.5 hours, how many miles apart are they now? Round to 2 decimal places.

Answer 3

368.65

Question 4

Use the figure below to find the missing side, c, when a = 9 , b = 8, and C = 35 . Round to 4 decimal places.

Question 5

In the figure below, when a = 8 , b = 7, and C = 44 , we have A = _____ . Round to 2 decimal places. If the triangle is not possible, enter "not possible".

Question 6

Use the figure below to find side a when Round to 2 decimal places.

Question 7

Use the figure below to find side a when . Round to 2 decimal places. If the triangle is not possible, enter "not possible".

Question 8

In the revolving door in the figure below, each panel is 0.9 meters long. How many meters is the distance along a straight line between A and D? Round to 2 decimal places.

Question 9

The Pentagon proposes to install a 5 panel revolving door with a panel width of 1.2 meters. A 5-star general wants to enter with a chart that is as wide as possible. How many meters wide is the widest chart that he can fit in the opening without bending it? In other words, how many meters is the distance across the opening? Round to 2 decimal places.

Question 10

Find A and c if . Round to two decimal places.

Question 11

Find the area of the triangle if . Round to two decimal places.

Question 12

To measure the height of a mountain, a person stands a certain distance from the base and measures the angle of elevation to the top of the mountain. This turns out to be . Moving 100 ft closer, the angle of elevation to the top of the mountain is . How tall is the mountain? Round your answer to 2 decimal places.

Question 13

Two ships leave port and head out to sea in straight lines at 1pm. It is noted that they are travelling away from each other at an angle of 41 . Ship A travels at 12 miles per hour and Ship B travels at 18 miles per hour. After how many hours are they 86 miles apart?

Question 14

Consider the triangle formed by the points . Find the measure of angle . Give your answer to 2 decimal places.

Question 15

.

Question 16

Let . Find the measure of angle . Give your answer to 2 decimal places.

Question 17

Find the area of the triangle if a = 6, b = 8, and c = 4. Round to two decimal places.

Question 18

Find the measures of the angles of the triangle if a = 6, b = 9, and c = 4. Round to two decimal places.

Question 19

In the following figure, suppose . Find a, and round your answer to two decimal places. If there are two possible answers, list both.

Question 20

In the following figure, suppose . Find A, and round your answer to two decimal places. If there are two possible answers, list both.

Question 21

If , find the following exactly.
A)
B)
C)

Question 22

If , find the following. Give your answers to 3 decimal places.

A)
B)
C)

Question 23

Let , find the following. Give your answers to 3 decimal places.

A)
B)
C)

Question 24

Let , find the following. Give your answers to 3 decimal places.


A)
B)
C)

Question 25

Evaluate the following. Give answers to 4 decimal places.

A)
B)
C)

Question 26

Solve for , an angle in a right triangle, if . Give the answer correct to 3 decimal places.

Question 27

Solve for , an angle in a right triangle, if . Give the answer correct to 3 decimal places.

Question 28

A 68 inch tall man casts a 102 inch long shadow. What is the angle of the sun? Give your answer to 3 decimal places.

Question 29

The grade of the road is 8.3%. What angle does the road make with the horizontal? Round your answer to 3 decimal places.

Question 30

A ramp is 101 feet long and the change in height of the ramp is 6 feet. What angle does the ramp form with the horizontal? Give your answer correct to 3 decimal places.

Question 31

Find , an angle in a right triangle, if . Give your answer to 3 decimal places.

Question 32

Find , an angle in a right triangle, if . Give your answer to 3 decimal places.

Question 33

Approximate the acute angle formed by the line and the . Give the answer correct to 3 decimal places.

Question 34

Solve for , an angle in a right triangle, if . Round your answer to 3 decimal places.

Question 35

Solve for , an angle in a right triangle, if . Find the answer correct to 2 decimal places.

Question 36

Kathleen starts at point A and walks 8 miles east to point B. Then, she walks 11 miles north to point C. What is the measure of angle ACB? Round to 2 decimal places.

Question 37

Evaluate the following. Round answers to 2 decimal places.

A)
B)

Question 38

Solve for , an angle in a right triangle, if . Round the answer to 2 decimal places.

Question 39

Approximate the acute angle made by the line and the . Round answer to 2 decimal places.

Question 40

Approximate the obtuse angle made by the line and the . Round answer to 2 decimal places.

Question 41

As P moves clockwise aroung the circle from A to B, what happens to ?

A) It first decreases and then increases.
B) It first increases and then decreases.
C) It increases.
D) It decreases.

Question 42

Is the period of greater than, less than, or the same as the period of ?

A) the same
B) greater
C) less

Question 43

How often do the graphs of and
cross?

A) never
B) once
C) infinitely often
D) twice

Question 44

Without a calculator, find the exact value of https://d2lvgg3v3hfg70.cloudfront.net/TB10073/. If it is undefined, enter "undefined".

Question 45

Find the following exactly using the figure given if and .

A)
B)
C)
D)
E)
F)

Question 46

Which of the following graphs have period 2 and amplitude 4?

A)
B)
C)
D)

Question 47

Suppose the table below is for a periodic function with period 3: Evaluate .

Question 48

Suppose the table below is for a periodic function with period 3: What is the next integer value n at which ?

Question 49

Graph a function with midline -1, amplitude 3, and period 4. Show at least two full periods.

Question 50

An animal population in a national park dropped from a high of 232,000 in 1943 to a low of 76,000 in 1989, and has risen since then. Scientists hypothesize that the population follows a sinusoidal cycle affected by predation and other environmental conditions, and that the caribou will again reach their previous high. Predict the next year when the population will again be 232,000.

Question 51

Find the following exactly using the figure given if and
.

A)
B)
C)
D)
E)
F)

Question 52

Suppose you are on a ferris wheel (that turns in a counter clockwise direction) and that your height, in meters, above the ground at time t, in minutes, is given by . How many minutes does one revolution take?

Question 53

Suppose you are on a ferris wheel (that turns in a counter clockwise direction) and that your height, in meters, above the ground at time t, in minutes, is given by . Your position on the wheel be at time t = 0 is _____ o'clock.

Question 54

Suppose you are on a ferris wheel (that turns in a counter clockwise direction) and that your height, in meters, above the ground at time t, in minutes, is given by . How many meters above the ground are you at time t = 0?

Question 55

Suppose and . What is if f is linear? Your answer will have b in it.

Question 56

Suppose and . What is if f is periodic with period 2a? Your answer will have b in it.

Question 57

Question 58

Question 59

A rope is attached to the top of a tree and to a stake in the ground. The angle of the rope with the ground is and the rope comes out 150 feet from the tree. How tall is the tree? Give your answer correct to 2 decimal places.

Question 60

Find the exact value of the following without a calculator. If it is undefined, enter "undefined".

A)
B)
C)

Question 61

Estimate the period of the following periodic function.

Question 62

Estimate the period of the following periodic function.

A)
B)
C) -1
D) -2

Question 63

Find the exact value of the following without a calculator. If it is undefined, enter "undefined".

A)
B)
C)

Question 64

Does the following function appear to be periodic with period less than or equal to 4?

Question 65

Does the following function appear to be periodic with period ?

Question 66

Find the exact value of the following without a calculator. If it is undefined, enter "undefined".

A)
B)
C)

Question 67

The proposed London ferris wheel is 135 meters in diameter and makes one revolution every 30 minutes. Let be the height above ground after t minutes of riding. What does represent?

A) The height on a ferris wheel that runs 2 times faster than the London one.
B) The height on a wheel which is 2 times larger in diameter than the London one.
C) C) The height of a person who boarded the London ferris wheel 2 minutes before you.
D) The height on the London ferris wheel with a loading platform 2 meters off the ground.

Question 68

The London ferris wheel is 135 meters in diameter and makes one revolution every 30 minutes. Let be the height above ground after t minutes of riding. Where is the midline for ?

Question 69

Find the following exactly using the figure given if and
.

A)
B)
C)
D)
E)
F)

Question 70

The graph below shows your height in meters t minutes after a ferris wheel ride begins. How many minutes are required for one complete revolution of the ferris wheel?

Question 71

A ferris wheel is 26 meters in diameter, and must be boarded from a platform that is 1.5 meters above the ground. The wheel makes one complete revolution every 6 minutes. At the initial time t = 0, you are in the 12:00 position. If gives your height above ground level t minutes after the initial time, the midline of is y = _____.

Question 72

A ferris wheel is 30 meters in diameter, and must be boarded from a platform that is 2.5 meters above the ground. The wheel makes one complete revolution every 8 minutes. At the initial time t = 0, you are in the 12:00 position. If gives your height above ground level t minutes after the initial time, what is the period of ?

Question 73

A vacationer sits all day on the corner of a pier in Boston Harbor and notices that at 9 am, when the water level is at its lowest, the water's depth is 1.5 feet. At 4 pm, the water has risen to its maximum depth of 11.5 feet. If the depth of the water level varies periodically, let
be the formula for the depth of the water, in feet, as a function of time t, in hours past 9 am. What is the period of the graph of ?

Question 74

Consider the following figure. If find a and c. Round your answers to 2 decimal places, if necessary.

Question 75

If and , find two different expressions for the exact value of a.

Question 76

If and
, find the following exactly.

A)
B)
C)

Question 77

Consider the following figure. If find a and b. Round your answers to 2 decimal places, if necessary

Question 78

If angle lies in Quadrant IV, name the quadrant in which the following angles lie :

A)
B)
C)
D)

Question 79

Find the area of the triangle given if and . Give your answer correct to 3 decimal places.

Question 80

Two ships start at the same port. Ship A travels due east at 11 mph. Ship B travels due north. After 3 hours, the ships are 60.75 miles apart. How fast was ship B traveling? Round your answer to the nearest whole number.