3. Trigonometry

Law Of Sines — Quiz

Test your understanding of law of sines with 5 practice questions.

Practice Questions

Question 1

Using the ambiguous SSA case, in triangle ABC with side a = 12, side b = 15, and angle A = 50°, what are the two possible measures of angle B?

Question 2

In a surveyor’s problem, points A and B are 40 m apart on one bank of a river. At a point C on the opposite bank, ∠CAB = 40° and ∠CBA = 55°. What is the distance AC (to the nearest tenth of a meter)?

Question 3

Given triangle ABC with b = 14, angle A = 45°, and side a = 10, how many distinct triangles satisfy these SSA conditions?

Question 4

In triangle ABC, ∠A = 20°, ∠B = 85°, and side a = 7 cm. What is the length of side c (to one decimal place)?

Question 5

In triangle ABC, the Law of Sines gives sin A/a = sin B/b = sin C/c. What does this common ratio equal in terms of the circumradius R?