Question

Please help with the question in the photo below.

Answer 1

Answer:

53.8°

Step-by-step explanation:

Use cosine law

67² = 72² + 76² - 2(72)(76)cosX

cosX = 719/1216

X = 53.75190075

Answer 2

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