Need help on solving this question about Triangles

Question

Find the length x. Round to the nearest tenth.

I know it shows my work but I don't believe I solved it correctly. By that I mean solving it in a Precaclulus way than a Tringometry way. Is there any other way in solving this other than how I showed it or would it be accepted in Precaculus? 

Answer 1

Step 1:

Solving triangle:

Find the side () of the triangle by using the Law of Sines.

The sum of three angles in a triangle  is .

.

Sine rule:

.

Consider .

.

The length .

Solution:

The length .