Name:_____________________________________
Review Sheet: Trig Applications
Date:_______ Period:______
Ms. Anderle
Review Sheet: Trig Applications
Law of Cosines
Given the following measures in ΔDEF, find the length of the third side to the nearest tenth.
1. e = 7, f = 8, m<D = 30
2. d = 10, e = 8, m<F = 60
3. d = 4, e = 8, m<F = 120
4. d = 3, f = 10, m<E= 120
5. d = 4, e = 9, m<F = 110
6. d = 5, e = 8, m<F = 40
The lengths of the sides of ΔRST are given. Find the greatest angle, to the nearest degree.
7. r = 4, s = 5, t = 6
8. r = 10, s = 13, t = 5
9. r = 3, s = 4, t = 2
10. Find, to the nearest degree, the measure of the base angle of an isosceles triangle whose sides
measure 14, 14, and 8 units.
Area of a Triangle
Find the area of ΔABC, rounded to three decimals. (remember the angle must be included)
1
11. a = 8, b = 9, sin 𝐶 =
12. a = b = 14, m<B = 75
13. b = 16, c = 18, m<A = 150
4
Find, to the nearest tenth, the area of parallelogram ABCD if sides, s1 and s2, and angle A have the
following measures.
14. s1 = 18, s2 = 14, m<A = 60
15. s1 = 23, s2 = 31, m<A = 42
Law of Sines
Find the indicated measures for ΔABC. Round lengths to the nearest centimeter and angles to the
nearest degree.
16. m<A = 45, m<B = 60, a = 8, b = ?
17. m<C = 75, m<A = 45, b = 9, a = ?
18. b = 13, a = 8, m<B = 22, m<A = ?
19. m<C = 95, m<A = 70, b = 3, a = ?
20. In ΔABC, the measurements of <A = 33°40' and <B = 53°20’ and BC = 17.4 cm. Find the length, in
centimeters of AC.
Ambiguous Case
For each of the following, first determine the number of triangles that can be constructed with the given
measures. Then find, if possible, the indicated measures to the nearest degree.
21. m<A = 140, b = 10, a = 3
22. m<A = 50, a = 13, b = 16
23. m<A = 58, b = 13, a = 17
Forces and Vectors
24. Two forces of 18 lb and 20 lb act on a body at an angle of 120. Find the magnitude of the resultant
force to the nearest tenth.
25. Two forces of 130 kg and 90 kg act on an object. The angle between the two forces is 54°. What is
the magnitude of the resultant force, to the nearest tenth?
26. Two forces of 2 N and 12 N act on an object. The angle between the two forces is 62°. What is the
magnitude of the resultant force, to the nearest tenth?