Questions

1) Refer to the figure below to answer the following questions: (a) What ratio represents “tan M”? (b) What ratio represents “cos M”? (c) What ratio represents “sin M”?

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2) Which ratio represents the sine of angle T?

a.) sin T = r / s

b.) sin T = t / s

c.) sin T = t / r

d.) sin T= r / t

3) Which ratio represents the tangent of angle T?

a.) tan T = r / s

b.) tan T = t / s

c.) tan T = t / r

d.) tan T= r / t

4) Which ratio represents the cosine of angle T?

a.) cos T = r / s

b.) cos T = t / s

c.) cos T = t / r

d.) cos T = r / t

5) Write a ratio to represent the “sin K”.

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6) Write a ratio to represent the “cos K”.

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7) Write a ratio to represent the “tan K”.

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8) Write a ratio to represent the “sin J”.

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9) Write a ratio to represent the “cos J”.

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10) Write a ratio to represent the “tan J”.

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11)

Use the table of trigonometric ratios, a scientific calculator, or a graphing calculator to evaluate the following trigonometric functions: (a) sin 30, (b) cos 45, (c) tan 80. Express each answer to the nearest ten thousandth (4 decimal places).

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12) Which equation can be used to determine the length of DF and what is DF to the nearest tenth?

a.) tan 40 = x / 10; x = 8.4

b.) cos 40 = 10 / x; x = 13.1

c.) sin 40 = x / 10; x = 6.4

d.) tan 40 = 10 / x; x = 11.9

13) sin x = 0.4067

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14) tan x = 0.9004

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15) cos x = 0.1564

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16) What is the measure of angle R in right triangle PQR shown below? Round the answer to the nearest tenth of a degree.

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17) What is the length of MP?

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18) What is the measure of angle T in right triangle SRT shown below? Round the answer to the nearest whole degree.

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19) An angle of elevation is formed with a line of sight that is elevated __________ a horizontal baseline.

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20) In the figure shown below, what is the name of the angle of elevation?

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21) Which Greek symbol represents “theta”? This symbol often represents angles of elevation or depression? State the letter of the correct answer.

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22) The angle of elevation from the bottom of one palm tree to the top of another palm tree that is 40 feet away is 55 degrees. How tall is the second palm tree? Round the answer to the nearest foot.

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23) A tree that is 35 feet high casts a 56-foot shadow. What is the measure of the angle of elevation that is created by the sun and the end of the shadow of the tree?

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24) A lighthouse rises 160 feet above sea level. The top of the lighthouse is sighted in at a 3-degree angle from a ship at sea. What is the distance between the ship and the lighthouse? Round the answer to the nearest foot.

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25) An angle of depression is formed with a line of sight that is depressed __________ a horizontal baseline.

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26) In the figure shown below, what is the name of the angle of depression?

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27) The angle of depression from the top of one building to the top of a nearby building is 15 degrees. The buildings are 75 feet apart. What is the difference between the heights of the buildings? Round the answer to the nearest tenth of a foot.

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28) Kara is standing on the edge of a 15-foot high diving board. Her friend, Sierra, is treading water 45 feet from a spot in the pool directly below Kara. What is the angle of depression from the edge of the diving board to the surface of the water where Sierra is located? Round the answer to the nearest degree.

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29) Which equation represents the Law of Sines for triangle ABC with sides "a", "b", and "c" opposite the corresponding angles, respectively? State the letter of the correct answer.

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30) What does the phrase “solve a triangle” mean?

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31) After solving a triangle, what check may be performed to determine if the lengths of the sides and the size of the angles opposite those sides are correct?

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32) Solve the triangle shown below. (Hint: Find the size of angle F and the values of “e” and “f”.)

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33) Solve the triangle shown below.

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34) Which equation represents the Law of Cosines for triangle ABC with sides “a”, “b”, and “c” opposite the corresponding angles, respectively? State the letter of the correct answer.

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35) Which equation could be used to find the measure of angle S? State the letter of the correct answer.

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36) Solve the triangle.

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37) Which equation could be used to find the value of “v”? State the letter of the correct answer.

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38) Solve the triangle.

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39) Logan wants to determine the distance across the river from points B to C. If she is able to determine the measures given on the map using surveyors’ tools, what is the distance between points B and C? Round the answer to the nearest tenth of a foot.

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40) Explain the solution to the previous problem.

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41) A forest ranger sights two possible fires from his lookout tower. With his equipment, he is able to determine that one fire is about 7 miles in a northeast direction, the other fire is about 5 miles east, and the angle between the two lines of sight from him is 58 degrees. How far apart are the two fires? Round the answer to the nearest tenth of a mile.

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