Think you’ve got your head wrapped around Analytical Trigonometry? Put your knowledge to
the test. Good luck — the Stickman is counting on you!
Q. What is the formula for the area of a triangle given two side measurements and an included angle?
A = ½ab cos C
A = ½ab sin C
A = ½ab
A = ½ab tan C
A = abC
Q. Find the area of a triangle with sides measuring 23 units and 27 units, with an included angle of 42°.
310.5 units2
13,041 units2
415.5 units2
207.8 units2
230.7 units2
Q. Find the area of a triangle with sides measuring 3 units and 5 units, with an included angle of 22°.
165 units2
330 units2
2.8 units2
5.6 units2
7.0 units2
Q. A triangle has sides measuring 4 and 8 units and has an area of 5 units2. What is the measurement of the angle between the two given sides?
8.9°
24.6°
4.5°
18.2°
71.8°
Q. A triangle has sides measuring 15 units and 12 units. If the angle opposite the side measuring 15 units is 53°, what is the measurement of the angle opposite the side measuring 12 units?
39.7°
86.7°
61.2°
50.3°
44.3°
Q. Which of these is a form of the Law of Cosines?
A = ½ab sin C
c sin A = a sin C
c2 = a2 + b2 – 2ab cos C
Q. A triangle has a 40° angle with the side opposite of it measuring 13 units long. If the triangle also has a 60° angle, what is the measurement of the side opposite of the 60° angle?
8.5 units
19.5 units
9.6 units
15.4 units
17.5 units
Q. A triangle has sides measuring 6, 7, and 10 units. What is the measurement of the angle opposite the side that is 6 units long?
51.7°
42.6°
36.2°
81.0°
53.8°
Q. A triangle has sides measuring 10 units and 11 units long, with an included angle of 34°. What is the measurement of the side opposite the 34° angle?
38.6 units
8.5 units
9.9 units
6.2 units
7.4 units
Q. A triangle has sides measuring 20 units and 22 units. If the angle opposite the third side is 31°, what is the measurement of the third side?
506.8 units
22.5 units
11.4 units
40.5 units
129.7 units