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    Question

    In a triangle ABC, angle A = 45 degrees, angle B = 60 degrees, and side a = 10 units. Find the length of side b.

    A 10√2 units Correct Answer Incorrect Answer
    B 5√6 units Correct Answer Incorrect Answer
    C 10(√3 + 1) units Correct Answer Incorrect Answer
    D 10(√3 - 1) units Correct Answer Incorrect Answer

    Solution

    First, find angle C. Since the angles in a triangle sum to 180 degrees, C = 180 - 45 - 60 = 75 degrees. Use the Law of Sines: sin(A)/a = sin(B)/b Substitute the given values: sin(45)/10 = sin(60)/b Solve for b: b = (10 * sin(60)) / sin(45) = 10√3 / (2/√2) = 5√3 * √2 = 5√6 Answer: (b)

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