Given △𝐴𝐵𝐶 with 𝐴=59°, 𝑎 =22 and 𝑏 =14 ...

Question

Given △𝐴𝐵𝐶 with 𝐴=59°, 𝑎 =22 and 𝑏 =14, determine whether the given measurements produce one triangle, two triangles or no triangle at all. If no triangle is possible, state this. If one triangle is possible, find ∠𝐵 and ∠𝐶. If two triangles are possible, find ∠𝐵 and ∠𝐶 for both triangles. Round your answer to the nearest whole number.

Hello! Pls help me sovve the triangle I am quite stuck!

Answer 1

The altitude on AB is 14 sin 59 = 10.629.

Therefore, there is a triangle including the angle at A and a triangle including the supplement of angle A.

Angle B can be determined from the law of sines and

then angle C can be determined by subtraction from 180 degrees.

Side AB can be determined either from the law of cosines or the law of sines.

If necessary the other triangle can be solved in a similar way.