Review the following concepts if needed:

- Trigonometry and More about Circles Help
- Primary Circular Functions Help
- Secondary Circular Functions Help
- The Right Triangle Model and The Pythagorean Theorem Help
- Pythagorean Theorem for Sine, Cosine, Secant and Tangent Help

**Trigonometry Practice Test**

A good score is eight correct. Answers are at the end of the article.

1 . Suppose you stand on a flat, level surface on a sunny morning. Your shadow is exactly four times as long as you are tall. What is the angle of the sun above the horizon, to the nearest degree?

(a) 14°

(b) 45°

(c) 76°

(d) More information is needed to answer this question.

2 . Suppose you stand on a flat, level surface on a sunny morning. The sun is at an angle of 50° above the horizon. You are exactly 160 centimeters (cm) tall. How long is your shadow, to the nearest centimeter?

(a) 122 cm

(b) 134 cm

(c) 190 cm

(d) More information is needed to answer this question.

3 . Imagine that you stand some distance away from a tall building with a flat roof. The earth in the vicinity of the building is flat and level. The angle between the horizon and the top of the building, as measured from a point at your feet, is 70.00°. The straight-line distance between your feet and the nearest point at the top of the building is 200 meters (m). How tall is the building, to the nearest meter?

(a) 115 m

(b) 188 m

(c) 213 m

(d) More information is needed to answer this question.

4 . One arc second is the equivalent of

(a) 1/60 of an arc minute

(b) 1/3600 of an arc minute

(c) 1/π of an arc minute

(d) 1/(2π) of an arc minute

5 . Approximately how many degrees are there in 1 rad?

(a) 32.7°

(b) 45°

(c) 57.3°

(d) None of the above.

6 . Suppose an almanac lists the latitude of your town as 35° 15′ 00″ N. This is equivalent to

(a) 35.15° N

(b) 35.25° N

(c) 35.50° N

(d) None of the above.

7 . What is the angle, in radians, representing revolution by 3/4 of a circle in a clockwise direction?

(a) 3π/4

(b) –3π/4

(c) 3π/2

(d) –3π/2

8 . The circumference of the earth is approximately 40,000 kilometers (km). What is the angular separation between two points 111 km apart, measured over the shortest possible path on the surface? Neglect irregularities in the terrain. Assume the earth is a perfect sphere.

(a) 1 rad

(b) 57.3°

(c) 1/360 rad

(d) 1°

9 . Suppose you live in a remote area and decide to install an outdoor antenna for receiving stereo FM broadcasts. You buy a support tower that is 20.00 meters (m) high. The installation guide recommends guying the tower from a point halfway up, and also from the top. The guide also recommends that all guy wires be sloped at angles no greater than 45° with respect to the horizontal. Suppose you install two sets of guy wires, one set from a point halfway up and the other set from the top. All guys are fastened to three anchors at ground level. Each guy anchor is at just the right distance from the base of the tower to make the top set of guy wires slant at precisely 45.00°. At what angle, to the nearest tenth of a degree and relative to the horizontal, does each of the lower-level guy wires slant? Assume the ground in the vicinity of the tower is flat and level.

(a) 22.5°

(b) 26.6°

(c) 30.0°

(d) More information is needed to answer this question.

10 . What is the largest possible value for the tangent of an angle?

(a) 1

(b) 90°

(c) π rad

(d) None of the above.

**Answers**

1 . a

2 . b

3 . b

4 . a

5 . c

6 . b

7 . d

8 . d

9 . b

10 . d

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