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    Question

    Determine the length of side BC if ∠BAC = 60⁰, AB= 10

    cm and AC = 15 cm.
    A 3√7 cm Correct Answer Incorrect Answer
    B 5√7 cm Correct Answer Incorrect Answer
    C 5√3 cm Correct Answer Incorrect Answer
    D 3√7 cm Correct Answer Incorrect Answer

    Solution

    ATQ,

    Image

    Cos A = (AC² + AB²- BC²) ÷ (2 X AC X AB)

    So, cos 60⁰= (15² + 10²- BC²) ÷ (2 X 15 X 10)

    OC, (1/2) = (225 + 100 - BC²) ÷ 300

    OC, 2 X (325 - BC²) = 300

    OC, 325 - BC² = 150

    OC, BC² = 175

    OC, BC = 5√7 cm

    But side cannot be negative.

    So, BC = 5√7 cm

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