Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 2 - No. 38)
In triangle ABC, if a=5, b=7, and angle C = 60°, what is the length of side c (using the Law of Cosines)?
√39
√43
√53
√59
Explanation
Applying the Law of Cosines: c^2 = a^2 + b^2 - 2abcosC = 5^2 + 7^2 - 2*5*7*cos(60°) = 25 + 49 - 70*0.5 = 39. c = √39, so the correct answer is approximately 6.24, or the closest value.
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