Triangle P R Q is shown. The length of P R is 4, the length of R Q is 6, and the length of P Q is 5. Law of cosines: a2 = b2 + c2 – 2bccos(A) Find the measure of AngleQ, the smallest angle in a triangle whose sides have lengths 4, 5, and 6. Round the measure to the nearest whole degree. 34° 41° 51° 56°

41°

Step-by-step explanation:

Using cosine rule : since the 3 sides are given

p = 6 ; q = 4 ; r = 5

q² = p² + r² - 2prCosQ

2prCosQ = p² + r² - q²

COS Q = (p² + r² - q²) / 2pr

Cos Q = (6² + 5² - 4²) / 2*6*5

Cos Q = 45 / 60

Cos Q = 0.75

Q = Cos^-1 (0.75)

Q = 41.409622

Q = 41° ( nearest degree)

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step-by-step explanation: