How to solve the triangle given one angle and 2 sides. I want help solving the problem not just an answer, thanks.

A. Use the law of cosines:

29² = 34² + c ² - 2•34•c cos(30.3°)

Use a calculator to solve for c ; notice this equation is quadratic, you get two possible solutions, c ≈ 5.973 ≈ 6 or c ≈ 52.738 ≈ 53.

Then use the law of sines to solve for the two possibles measures of angle C :

sin(30.3°)/29 = sin(C )/c

sin(C ) = c sin(30.3°)/29

sin(C ) ≈ 0.1039   or   sin(C ) ≈ 0.9175

C ≈ 6.0°   or   C ≈ 66.6°

The interior angles of any triangle sum to 180°, so the remaining angle has measure either

B = 180° - 30.3° - C

B ≈ 143.7°   or   B ≈ 83.1°

So to recap,

B ≈ 143.7°, C ≈ 6.0°, c ≈ 6

and

B ≈ 83.1°, C ≈ 66.6°, c ≈ 53

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