Question

Solve the triangle.

A = 52°, b = 14, c = 6

Answer Choices:

a ≈ 14.9, C ≈ 24.2, B ≈ 103.8

a ≈ 11.3, C ≈ 24.2, B ≈ 103.8

a ≈ 14.9, C ≈ 28.2, B ≈ 99.8

No triangles possible

Answer 1

a ≈ 11.3, C ≈ 24.2, B ≈ 103.8

Explanation:

The information A = 52°, b = 14, c = 6 lends itself to solution using the Law of Cosines: a^2 = b^2 + c^2 - 2bc cos A.

Here, a^2 = 14^2 + 6^2 - 2(14)(6) cos 52 degrees, or

= 196 + 36 - 168 (0.616)

= 120.57

Taking the positive square root of this results in a = 11.3.

This corresponds to the second answer choice: a ≈ 11.3, C ≈ 24.2, B ≈ 103.8