Geometry Trigonometry & Applications 3

Question 1

Using the Law of Sines, if a = 8, angle A = 30°, and angle B = 45°, which sets up side b?

Accepted Answer

b = 8 sin 45° / sin 30°

Answer

By the Law of Sines a/sin A = b/sin B, so b = 8 sin 45°/sin 30°.

Question 2

The Law of Cosines c² = a² + b² − 2ab cos C reduces to the Pythagorean theorem when C equals what?

Accepted Answer

90°

Answer

At C = 90°, cos C = 0, leaving c² = a² + b².

Question 3

In triangle with sides a = 5, b = 7 and included angle C = 60°, what is c²?

Accepted Answer

39

Answer

c² = 25 + 49 − 2(5)(7)(0.5) = 74 − 35 = 39.

Question 4

What is the area of a triangle with sides 6 and 10 and an included angle of 30°?

Accepted Answer

15

Answer

Area = ½·6·10·sin 30° = ½·60·0.5 = 15.

Question 5

When is the Law of Cosines preferred over the Law of Sines?

Accepted Answer

Given SAS or SSS

Answer

The Law of Cosines works directly with SAS or SSS configurations.

Geometry Practice Test