Question

How do you solve the triangle ABC, given a=22, A=50, c=27?

Answer 1

To 'solve' a triangle means to find all the missing values for the sides and angles. In this case, the lengths of `2` sides and the size of `1` angle are given, we have to find the size of the `3 rd` side and the other `2` angles.

`color(green)(hat C = 70, hat B = 60, b = 24.87`

Explanation:

`sin C = (c sin A) / a = (27 sin 50) / 22 = 0.9401`

`hat C = sin ^-1 0.9401 = 70^@`

`hat B = 180 - 50 - 70 = 60^@`

`b = (a * sin B) / sin A = (22 * sin 60) / sin 50 = 24.87`