Given △𝐴𝐵𝐶 with 𝑎 =4, 𝑏 =8 and 𝑐 =11, find ∠𝐴. Round your answer to the nearest whole number.

Question

Given △𝐴𝐵𝐶 with 𝑎 =4, 𝑏 =8 and 𝑐 =11, find ∠𝐴. Round your answer to the nearest whole number.

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Answer 1

By Cosine Law: cosA = (b² + c² - a²)/(2bc) = (64 + 121 - 16)/(2·8·11) = 169/176

∠A = cos^-1(169/176) = 16°

Answer 2

For this problem, since we know all 3 sides, the law of cosines can be used to determine the angle.

cos(A) = (b² + c² - a²)/2bc = (8² + 11² - 4²)/(2(8)(11))

cos(A) = (64 + 121 - 16)/176 = 169/176 = 0.96

Therefore ∠A = cos^-1(0.96) = 16.3°

Answer 3

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