Law of cosines: a2 = b2 + c2 – 2bccos(A) Find the measure of Q, 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°
Question
Answer:
a² = b² + c² – 2bccos(A)The smallest angle is across the smallest side, so
4²=5²+6²-2*5*6*cos(Q)
16=25+36-60*cos(Q)
16-36-25=-60*cos(Q)
45=60*cos(Q)
cos(Q)=45/60
Q=cos⁻¹(45/60) ≈41⁰
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11 months ago
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