Solving a triangle using different formulas

Question

Solve for the triangle (find all angles and sides). PLEASE USE DIFFERENT FORMULAS, NOT ONLY SINE LAW.

Answer 1

Since we start with two sides and an angle opposite one of the sides, we first have to use the sin law

All calculations are done via calculator, but results displayed are via rounding.

sin 50°/7 = sin A/8

sin A = 8 sin 50°/7

A = arcsin(8 (sin 50°)/7) = 61.1° or

A = 180° - 61.1° = 118.9°

Then, the third angle is

180° - 50° - 61.1° = 68.9°

Alternatively, the third angle is 180° - 50° - 118.9° = 11.1°

If we want to use a different law, we can use the cosine law.

a^2 = b^2 + c^2 - 2bc cos A

Thus, the third side is

a = sqrt(7^2+8^2 - 2*7*8 * cos(68.9°)) = 8.5

Alternatively, the third side is a = sqrt(7^2+8^2 - 2*7*8 * cos(11.1°)) = 1.8