∠A = 106.3°, ∠B = 20.6°, ∠C = 53.1°
<u>Step-by-step explanation:</u>
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°
