Find the area of the triangle with the given measurements: a=7, 𝛼 = 45°, 𝛾 = 60°.

Question

(To the extent possible use standard angles to simplify your responses. When necessary express your answers using the functions sin, cos, sin−1, cos−1. If there is no solution enter IMPOSSIBLE.)

Answer 1

Using standard convention in writing the data
You have triangle ABC, with angle A = 45°, and a = 7
angle B = 60°, which would make angle C = 75°

I can find AB using the sine law:
AB/sin60 = 7/sin45
AB = 7sin60/sin45 = 7(√3/2) / (1/√2)
= (7√3/2)(√2/1) = 7√6 / 2

Now you have 2 sides and the contained angle, just like in the
previous problem I did for you.

Repeat those steps to find the area