Download ExamView - Unit 6 Review.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
Unit 6 PreCalculus Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Find the degree measure of the angle:
a.
b.
c.
d.
π
15
rad.
12°
6°
16°
27°
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2. The measure of the angle 330° in standard position is given. Find two positive angles and two negative
angles that are coterminal with the given angle.
a. 426°, 786°, –294°, –654°
b. 670°, 1060°, –70°, –345°
c. 710°, 1020°, –50°, –360°
d. 690°, 1050°, –30°, –390°
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3. Find an angle between 0° and 360° that is coterminal with the angle: –2°.
a. 313°
b. 338°
c. 356°
d. 358°
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4. Find an angle between 0° and 360° that is coterminal with the angle 2595°.
a. 49°
b. 43°
c. 95°
d. 75°
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Name: ________________________
____
ID: A
5. Find x correct to one decimal place.
y = 60
a. 69.3
b. 66.2
c. 76.4
____
6. The angle of elevation to the top of a particular skyscraper in New York is found to be 12° from the ground
at a distance of 1.3 mi from the base of the building. Using this information, find the height of the skyscraper.
a. 1459 ft
b. 1560 ft
c. 2918 ft
____
7. A water tower is located x = 350 ft from a building (see the figure). From a window in the building it is
observed that the angle of elevation to the top of the tower is 39° and the angle of depression to the bottom of
the tower is 25°. How tall is the tower (t)? How high is the window (w)?
a.
b.
c.
t = 39 ft; w = 25 ft
t = 447 ft; w = 163 ft
t = 163 ft; w = 447 ft
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Name: ________________________
____
8. When the moon is exactly half full, the earth, moon, and sun form a right angle (see the illustration). At that
time the angle formed by the sun, earth, and moon is measured to be 89.75°. If the distance from the earth to
the moon is 235000 mi, estimate the distance from the earth to the sun.
a.
b.
c.
d.
____
ID: A
54093204 mi
53858204 mi
235000 mi
53623204 mi
9. Find sin 224°.
a. –0.6947
b. 0.6947
c. No correct answer
____ 10. Find cot –186°.
a. –9.51
b. No correct answer
c. –0.11
____ 11. Choose the value of cos θ from the information: csc θ = 6, θ in quadrant I.
a.
b.
c.
d.
−
35
6
35
6
1
6
No correct answer
____ 12. Find the area of an equilateral triangle with sides of length 5.
a. 21.651
b. No correct answer
c. 6.250
d. 10.825
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Name: ________________________
ID: A
____ 13. Solve for x correct to one decimal place.
a.
b.
c.
d.
e.
692.8
477.8
367.6
173.2
519.6
____ 14. Find the exact value of the expression.
(cos30°) − (sin30°)
2
a.
b.
c.
1
4
3
2
3
4
3
4
d.
e.
2
1
2
____ 15. A 78-ft tree casts a shadow that is 100 ft long. What is the angle of elevation of the sun?
a.
b.
c.
d.
e.
46.57°
14.15°
11.85°
34.62°
none of these
4
Name: ________________________
ID: A
____ 16. A 84-ft tree casts a shadow that is 47 ft long. What is the angle of elevation of the sun?
a.
b.
c.
d.
e.
19.96°
60.77°
10.42°
10.97°
21.05°
____ 17. Use the Law of Sines to find x. Let c =21, ∠A = 58°.
a.
b.
c.
d.
24
25
46
23
____ 18. Use the Law of Sines to find angle C. Let a = 28, and c = 13.
a.
b.
c.
d.
24°
25°
23°
30°
5
Name: ________________________
ID: A
____ 19. The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which
are 51 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are
measured to be ∠m = 85.5°, ∠k = 79.8°.
(a) How far is the satellite from station A?
(b) How high is the satellite above the ground?
a.
b.
c.
d.
The distance of the satellite from station A = 505.4, the satellite is high above the ground
as 503.8.
The distance of the satellite from station A = 525.4, the satellite is high above the ground
as 514.8.
The distance of the satellite from station A = 511.4, the satellite is high above the ground
as 493.8.
The distance of the satellite from station A = 473.4, the satellite is high above the ground
as 481.8.
____ 20. Solve triangle ABC, if a = 17, b = 10, and ∠C = 117°.
a.
b.
c.
d.
c = 23.31, ∠A = 35.02°, ∠B = 27.98°
c = 23.31, ∠A = 40.53°, ∠B = 19.47°
c = 28.31, ∠A = 43.53°, ∠B = 22.47°
c = 23.31, ∠A = 40.53°, ∠B = 22.47°
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Name: ________________________
ID: A
____ 21. Find the indicated side x if b = 6 , a = 33°, y = 70°. (Use either the Law of Sines or the Law of Cosines, as
appropriate.)
a.
b.
c.
d.
22.369
14.527
3.354
5.164
____ 22. A 50 foot tower is located on the side of a mountain that is inclined 35° to the horizontal. A guy wire is to be
attached to the top of the tower and anchored at a point 145 feet downhill from the base of the tower. Find
the shortest length of wire needed.
a.
b.
c.
d.
249.82 ft
107.92 ft
214.13 ft
178.44 ft
Numeric Response
1. The area of a circle is 84 cm2 . Find the area of a sector of this circle that subtends a central angle of
__________ cm 2
7
π
6
rad.
Name: ________________________
ID: A
2. Find the side labeled x. State your answer correct to five decimal places.
x = __________
Short Answer
1. Find the values of the trigonometric functions of θ from the information given.
tan θ = 6, sin θ > 0
(a) sinθ
(b) cosθ
(c) cscθ
(d) secθ
(e) cotθ
2. Sketch the triangle and then solve the triangle using the Law of Sines. Please round the answer to the nearest
tenth.
∠A = 23°, ∠B = 100°, c = 50
∠ C = __________ °
a = __________
b = __________
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ID: A
Unit 6 PreCalculus Review
Answer Section
MULTIPLE CHOICE
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NUMERIC RESPONSE
1. ANS: 7
PTS: 1
2. ANS: 31.40177
PTS: 1
SHORT ANSWER
1. ANS:
6
;
37
1
;
37
37
;
6
PTS: 1
1
ID: A
2. ANS:
57; 23.3; 58.7
PTS: 1
2