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

b = 8 sin 30° / sin 45°

Answer

b = 8 / (sin 45° sin 30°)

Answer

b = 8 sin 30° sin 45°

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

45°

Answer

60°

Answer

0°

Question 3

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

Accepted Answer

39

Answer

74

Answer

109

Answer

35

Question 4

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

Accepted Answer

15

Answer

30

Answer

60

Answer

7.5

Question 5

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

Accepted Answer

Given SAS or SSS

Answer

Given two angles and a side

Answer

Given a right angle only

Answer

Given only one side

Question 6

In triangle ABC, angle A = 40°, angle B = 60°. What is angle C?

Accepted Answer

80°

Answer

100°

Answer

70°

Answer

60°

Question 7

The ambiguous case (two possible triangles) can occur with which given information?

Accepted Answer

SSA

Answer

SAS

Answer

ASA

Answer

SSS