Chapter 6 review.notebook - Steilacoom

Chapter 6 review.notebook

pg. 440 #52

Find the angle in the figure.

10

5

pg. 441

#70 How many wheel revolutions will a car wheel of diameter 30 in. make as the car travels a distance of one mile?

pg. 449 #29

Evaluate the expression without using a calculator.

pg. 475

#43 The elongation of a planet is the angle formed by the planet, earth, and sun (see the figure). It is known that the distance from the sun to Venus is 0.723 AU. At a certain time the elongation of Venus is found to be 39.4o. Find the possible distances from the earth to Venus at that time in astronomical units (AU).

Venus Venus

1 AU

Earth

pg. 488 #19

Find the area of the shaded region.

72o 10 m

pg. 488 #19

Find the perimeter of the shaded region.

72o 10 m

Chapter 6 review.notebook

pg 449 Evaluate the expression without using a calculator

# 30

pg. 481

#35 Find the area of the figure, rounded to two decimals.

6

5

100o

7 8

pg. 481 #36 Find the area of the figure, rounded to two decimals.

3

3

4

4

60o

pg 468 #39

An observer views the space shuttle from a distance of 2 mi from the launch pad.

a. Express the height of the space shuttle as a function of the angle of elevation .

b. Express the angle of elevation as a function of the height h of the space shuttle.

h

2mi

pg 488

#21 Two wires tether a balloon to the ground. How high is the balloon above the ground?

h

75o

85o

100 ft

pg. 449 #45 Express the length x in terms of the trigonometric ratios of .

10

x

Chapter 6 review.notebook

pg. 473 #19

Solve for all possible triangles that satisfy the given conditions.

a = 28, b = 15, A = 110o

pg. 475 #42 A water tower 30 m tall is located at the top of a hill. From a distance

of 120 m down the hill, it is observed that the angle formed between the top and base of the tower is 8o. Find the angle of inclination of the hill.

30 m

8o

120 m

pg. 450

#54

A woman standing on a hill sees a flagpole that she knows is 60 ft tall. The angle of depression to the bottom of the pole is 14o, and the angle

of elevation to the top of the pole is 18o. Find her distance x from the

pole.

18o

x

14o

pg. 480 #6

C

Determine the indicated side x.

x

8 B

2 88o A

pg. 480 #12

Solve triangle ABC.

C 12

40 A

44 B

pg. 474 #29

Find BCD and DCA.

20

B

C

28 20

30o

D

A

Chapter 6 review.notebook

pg. 468 #43 For a wave to be surfable, it can't break all at once. Robert

Guza and Tony Bowen have shown that a wave has a surfable shower if it hits the shoreline at an angle given by

where is the angle at which the beach slopes down and where n = 0, 1, 2, ... a) For = 10o, find when n = 3.

b) For = 15o, find when n = 2, 3, and 4. Explain why the formula does not give a value for when n = 0 or 1.

pg. 473 #11

C

Solve the triangle.

A 46o

65

20o

B

pg. 473 #6

Solve for .

C

67o 56.3

B

A

80.2

pg. 473 #21 Solve for all possible triangles that satisfy the given

conditions.

a = 20, c = 42, C = 38o

pg. 448 #24

Find the other trigonometric ratios of .

pg. 474 #28

Solve for all possible triangles that satisfy the given conditions.

b = 73, c = 82, B = 58o

Chapter 6 review.notebook

pg. 460

#59

Find the area of the shaded region in the figure.

pg. 460 #60

Find the area of the shaded region in the figure.

12

pg. 460

#44

Write the first trigonometric function in terms of

the second for in the given quadrant.

in Quadrant III

pg. 461

#71 Rainbows are created when sunlight of different wavelengths (colors) is refracted and reflected in raindrops. The angle of

elevation of a rainbow is always the same. It can be shown

that

, where

and = 59.4o and k = 1.33 is the index of refraction of water. Use the given information to find the angle of elevation of a rainbow.

pg. 450

#60 To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75o from the horizontal. An observer 600 m away measures the angle of elevation to the spot of light to be 45o. Find the height h of the cloud cover.

h

45o

75o

600 m

pg. 442 #86 The sprockets and chain of a bicycle are shown in the figure. The

pedal sprocket has a radius of 4 in., the wheel sprocket a radius of 2 in., and the wheel of a radius of 13 in. The cyclist pedals at 40 rpm. a) Find the angular speed of the wheel sprocket.

b) Find the speed of the bicycle.

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