Trigonometry Laws of Sines and Cosines 2

Question 1

In triangle ABC, a = 8, b = 11, and angle A = 35°. Using the Law of Sines, which equation correctly finds angle B?

Accepted Answer

sin B = 11 · sin 35° / 8

Answer

sin B / 8 = sin 35° / 11

Answer

sin B / 11 = sin 35° / 8

Answer

sin B = 8 · sin 35° / 11

Question 2

A triangle has sides a = 5, b = 7, c = 9. Which formula correctly begins the calculation to find angle C using the Law of Cosines?

Accepted Answer

cos C = (a² + b² − c²) / (2ab)

Answer

c² = a² + b² + 2ab·cos C

Answer

cos C = (a² + b² + c²) / (2ab)

Answer

cos C = (c² − a² − b²) / (2ab)

Question 3

In an obtuse triangle where angle B > 90°, the Law of Sines may produce an ambiguous case. When is angle B guaranteed to be obtuse?

Accepted Answer

When b is the longest side and b > a

Answer

When sin B < 0.5

Answer

When b > a and the calculated sin B yields two possible angles

Answer

The Law of Sines always produces a unique obtuse angle

Question 4

Using the Law of Cosines, what is the length of side c in a triangle where a = 6, b = 8, and C = 60°?

Accepted Answer

√52

Answer

√148

Answer

√28

Answer

√100

Question 5

Triangle PQR has angle P = 50°, angle Q = 80°, and side p = 12. What is the length of side q?

Accepted Answer

q = 12·sin 80° / sin 50°

Answer

q = 12·sin 50° / sin 80°

Answer

q = sin 80° / (12·sin 50°)

Answer

q = 12·sin 50° / sin 130°

Question 6

Two ships leave a port; one travels 30 km on a bearing of 40° and the other travels 45 km on a bearing of 100°. What angle between their paths should you use in the Law of Cosines?

Accepted Answer

60°

Answer

40°

Answer

100°

Answer

140°

Question 7

For which given information set is the Law of Cosines required (Law of Sines cannot be used directly)?

Accepted Answer

SSS (three sides known)

Answer

AAS (two angles and a non-included side)

Answer

ASA (two angles and the included side)

Answer

AAA (all three angles known)