1.
(Points: 0.5)
Solve the problem.

A photographer points a camera at a window in a nearby building forming an angle of 42° with the camera platform. If the camera is 52 m from the building, how high above the platform is the window, to the nearest hundredth of a meter?




a. 0.9 m
b. 57.75 m
c. 1.11 m
d. 46.82 m



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2.
(Points: 0.5)
Find all the complex roots. Write the answer in the indicated form.

The complex square roots of 100(cos 60° + i sin 60°) (polar form)




a. 10(cos 30° + i sin 30°), 10(cos 210° + i sin 210°)
b. 10(cos 60° + i sin 60°), 10(cos 120° + i sin 120°)
c. 10(cos 60° + i sin 60°), -10(cos 120° + i sin 120°)
d. 10(cos 30° + i sin 30°), 120(cos 210° + i sin 210°)



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3.
(Points: 0.5)
Determine whether or not the vectors are perpendicular.

< -2, 6 > and < 5, -5 >




a. No
b. Yes



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4.
(Points: 0.5)
Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.

a = 9
b = 14
c = 15




a. A = 34°, B = 66°, C = 80°
b. A = 36°, B = 66°, C = 78°
c. A = 38°, B = 64°, C = 78°
d. no triangle



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5.
(Points: 0.5)
Find the area of the triangle. If necessary, round the answer to two decimal places.

Find the area of a triagle with sides 4, 6, and 9. Do not assume that it is a right triangle.









a. 192.48
b. 44.16
c. 3.1
d. 9.56



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6.
(Points: 0.5)
Solve the problem.

A force of 632 lb is required to pull a boat up a ramp inclined at 16.0° with the horizontal. How much does the boat weigh?




a. 2900 lb
b. 608 lb
c. 616 lb
d. 2290 lb



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7.
(Points: 0.5)
Use DeMoivre's Theorem to find the indicated power of the complex number. Write answer in rectangular form.

(cos 30° + i sin 30°)24




a. 1
b. -1
c. i
d. -i



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8.
(Points: 0.5)
Solve the problem.

Two sailboats leave a harbor in the Bahamas at the same time. The first sails at 20 mph in a direction 330°. The second sails at 34 mph in a direction 220°. Assuming that both boats maintain speed and heading, after 2 hours, how far apart are the boats?




a. 89.9 miles
b. 95.9 miles
c. 70.5 miles
d. 58.5 miles



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9.
(Points: 0.5)
Solve the problem.

A child throws a ball with a speed of 6 feet per second at an angle of 25° with the horizontal. Express the vector described in terms of i and j. If exact values are not possible, round components to 3 decimals.




a. 2.536i + 5.438j
b. 5.438i + 2.536j
c. -5.438i + 2.536j
d. 2.536i - 5.438j



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10.
(Points: 0.5)
Solve the problem.

A radio transmission tower is 240 feet tall. How long should a guy wire be if it is to be attached 6 feet from the top and is to make an angle of 23° with the ground? Give your answer to the nearest tenth of a foot.




a. 598.9 ft
b. 614.2 ft
c. 260.7 ft
d. 254.2 ft



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