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# Global Trigonometry Practice Test

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By McGraw-Hill Professional
Updated on Oct 3, 2011

Review the following concepts if needed:

## Global Trigonometry Practice Test

A good score is eight correct.

1. When the angular lengths of two sides of a spherical triangle are known, and the measure of the spherical angle between those two sides is also known, then the angular length of the side opposite the known spherical angle can be found using

(a) the Pythagorean theorem

(b) latitude and longitude

(d) none of the above

2. Suppose the universe is a gigantic sphere with a circumference of 2.4 × 10 10 parsecs (pc). How long is a geodesic arc on the surface of that sphere whose angular measure is equal to 1° 0′ 0″?

(a) 1.33 × 10 7 pc

(b) 6.67 × 10 7 pc

(c) 3.82 × 10 9 pc

(d) 7.64 × 10 9 pc

3. Suppose two shortwave radio signals arrive at a receiving station after having traveled thousands of kilometers along geodesic paths. One signal comes from azimuth 60° and the other comes from azimuth 140°. The difference between these azimuth angles, 80°, is an example of

(a) the law of sines

(b) the law of cosines

(d) a spherical angle

4. Suppose an aircraft pilot wants to fly a great-circle route from point R to point S , where:

Lat R = +45.00° Lon R = –97.00° Lat S = +8.00° Lon S = +55.00°

The length of a geodesic (great-circle route) between these two points is approximately

(a) 10,500 kilometers

(b) 12,000 kilometers

(c) 13,500 kilometers

(d) 17,500 kilometers

5. Consider a four-sided polygon on the surface of the earth, whose vertices Q, R, S, and T are at the following latitudes and longitudes:

Lat Q = +30° 0′ 0″ Lon Q = 0° 0′ 0″ Lat R = + 30° 0′ 0″ Lon R = + 90° 0′ 0″ Lat S = + 30° 0′ 0″ Lon S = 180° 0′ 0″ Lat T = + 30° 0′ 0″ Lon T = –90° 0′ 0″

This is a spherical square. The measure of each interior spherical angle of this spherical square is:

(a) less than 90°

(b) equal to 90°

(c) more than 90°

6. Suppose a spherical polygon has vertices at the following locations on the earth’s surface:

Lat Q = 0° 0′ 0″ Lon Q = +24° 0′ 0″ Lat R = 0° 0′ 0″ Lon R = –110° 0′ 0″ Lat S = 0° 0′ 0″ Lon S = +134° 0′ 0″

The angular length of the great-circle arc QR, to the nearest hundredth of a radian, is

7. The sum of the measures of the interior spherical angles of the spherical polygon described in Question 6, to the nearest degree, is

(a) 540°

(b) 312°

(c) 132°

(d) 48°

8. Consider a spherical equilateral triangle on the earth’s surface with each side measuring exactly 11,000 kilometers in length. What is the measure of each interior spherical angle of this spherical triangle to the nearest degree?

(a) 101°

(b) 79°

(c) 60°

9. Suppose Q and R are two points on the earth that are widely separated. Imagine that a shortwave radio transmitter is located at point Q, and its signal is received at point R after propagating along two great-circle arcs: one arc representing the short path and the other arc representing the long path. The two signals arrive at point R from

(a) the same point of the compass

(b) points of the compass that differ by 90°

(c) points of the compass that differ by 180°

(d) all points of the compass simultaneously

10. The sum of the measures of the interior angles of an equilateral spherical triangle is always greater than

(a) 540°

(b) 360°

(c) 180°

(d) none of the above

1. d

2. b

3. d

4. c

5. c

6. b

7. a

8. a

9. c

10. c

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