Trigonometry help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

 

In the triangle ABC if angle A is 20 degrees, angle B is 35 degrees and the side between (side C) them is 100, what is the approximate length of side a?

Answer 1

A = 20°, B = 35° and the side between (side c) them is 100.

First to find angle C. Since the sum of the angles in any triangle is 180°.

We have A + B + C = 180

20 + 35 + C = 180

55 + C = 180

Subtract 55 from each side.

C = 180 - 55 = 125°

To find length of side a, we use the following two ratios given the law of sines.

[a/sin(A)] = [c/sin(C)]

[a/sin(20°)] = [100/sin(125°)]

Trigonometric table in sin(20°) = 0.3420 and sin(125°) = 0.8191.

[a/(0.3420)] = [100/(0.8191)]

Multiply each side by 0.3420.

a = 100(0.3420)/(0.8191)

a = 34.2/0.8191

a = 41.75

The approximate length of side a = 41.71