Question

Solve the triangle.

A = 50°, b = 13, c = 6

choices:
a ≈ 10.2, C ≈ 26.3, B ≈ 103.7

a ≈ 14, C ≈ 26.3, B ≈ 103.7

No triangles possible

a ≈ 14, C ≈ 30.3, B ≈ 99.7

Answer 1

First Choice

Step-by-step explanation:

Too long to write out.

Answer 2

a = sqrt(b^2 + c^2 - 2bc cosA) = sqrt(13^2 + 6^2 - 2 * 13 * 6 * cos 50) = sqrt(169 + 36 - 156 cos 50) ≈ sqrt(205 - 100.3) ≈ sqrt(104.7) ≈ 10.2
a ≈ 10.2

c / sin C = a / sin A
sin C = c sin A / a = 6 sin 50 / 10.2 ≈ 0.4491
C = arcsin(0.4491) ≈ 26.7
C ≈ 26.7°

B = 180 - A - C ≈ 180 - 50 - 26.7 ≈ 103.3
B ≈ 103.3°