Question

Consider a triangle ABC . Suppose that B=126°, a=38, and c=22. Solve the triangle.

Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.

Answer 1

b = 54; A = 34.7°; C = 19.3°

Explanation:

To solve the triangle means that we have to calculate the values of the missing angles and the missing sides.

We are given;

B = 126°, a = 38, and c = 22

Using law of cosines, we can find side b.

So;

b² = a² + c² - 2ac*cosB

Thus;

b² = 38² + 22² - 2(38 × 22)cos 126

b² = 1444 + 484 - 1672(-0.5878)

b² = 2910.8016

b = √2910.8016

b = 53.9518 ≈ 54

Using Law of sines, we can find the other 2 angles a and c.

Thus;

a/sin A = b/sinB = c/sinC

Thus, for A;

a/sin A = b/sin B

38/sin A = 53.9518/sin 126

sinA = (38 × sin 126)/53.9518

sinA = 0.5698

A = sin^(-1) 0.5698

A = 34.7363° ≈ 34.7°

Likewise;

b/sinB = c/sinC

53.9518/sin 126 = 22/sinC

sinC = (22 × sin 126)/53.9518

sinC = 0.3299

C = sin^(-1) 0.3299

C = 19.2627 ≈ 19.3°