Question

Solve the triangle.

Answer 1

∠A = 106.3°, ∠B = 20.6°, ∠C = 53.1°

Step-by-step explanation:

In a ΔABC, the sides opposite to the angle A is a, angle B is b, and angle C is c. a = 60 , b= 22, c = 50

We can find any one angle by cosine rule,

a² = b² + c² - 2 bc cos (A)

60² = 22² + 50² - 2(22)(50) cos A

3600 = 484 + 2500 - 2200 cos A

3600 = 2984 - 2200 cos A

3600 - 2984 = -2200 cos A

616 = -2200 cos A

cos A = 616/ -2200 = -0.28

A = cos⁻¹ (-0.28) = 106.3°

Now we can use sine rule to find angle B as,

sin A/ a = sin B / b

sin  106.3° / 60 = sin B / 22

sin B = 22 × sin  106.3° / 60

 B = sin⁻¹ (22 × sin  106.3° / 60 ) = 20.6°

As we know the sum of angles in a triangle is 180°.

∠A + ∠B + ∠C = 180°

106.3° + 20.6° + ∠C = 180°

126.9° + ∠C = 180°

∠C = 180° - 126.9° = 53.1°