Answer:
Step-by-step explanation:
Since we know the three sides and no angle is known, we would apply the law of Cosines which is expressed as
a² = b² + c² - 2abCosA
Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes
SR² = SQ² + QR² - 2(SQ × QR)CosQ
67² = 76² + 72² - 2(76 × 72)CosQ
4489 = 5776 + 5184 - 2(5472)CosQ
4489 = 10960 - 10944CosQ
10944CosQ = 10960 - 4489
10944CosQ = 6471
CosQ = 6471/10944
CosQ = 0.59
Q = Cos^(- 1)0.59
Q = 53.8° to the nearest tenth
