Question

    If △ ABC is right angled at B, AB = 12 cm and ∠ CAB

    = 60°, determine the length of BC.
    A 24√3 cm Correct Answer Incorrect Answer
    B 12 cm Correct Answer Incorrect Answer
    C 12√2 cm Correct Answer Incorrect Answer
    D 12√3 cm Correct Answer Incorrect Answer

    Solution

    ATQ, Given, Δ ABC is right-angled at B. AB = 12 cm and ∠CAB = 60° To angle ∠CAB, AB is the adjacent side. AC is the hypotenuse of the triangle. So, we will use cos ∠CAB. cos ∠CAB = cos 60° = AB/AC= 1/2 ∴ 1/2 = 12/AC => AC = 2 × 12 = 24 cm So, AC = 24 cm To angle ∠CAB, AB is the adjacent side and BC is the opposite side. So, we will use tan ∠CAB tan ∠CAB = tan 60° = BC/AB => √3 = (BC/12) So, BC = (12 × √3)cm = 12√3cm

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