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22 June, 11:17

Given: ∆ABC, m∠C = 90° m∠BAC = 2m∠ABC BC = 24, AL - ∠ bisector Find: AL

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  1. 22 June, 15:07
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    The answer is that AL is equal to 16.

    Given that in triangle ABC, m∠C=90,

    it means m∠A + ∠B = m∠BAC + m∠ABC = 90

    m∠ABC = 90 - m∠BAC

    Also given that; m∠BAC = 2m∠ABC

    So,

    m∠BAC = 2 (90 - m∠BAC) = 180 - 2m∠BAC

    m∠BAC + 2m∠BAC = 180

    3m∠BAC = 180

    m∠BAC=180/3 = 60

    m∠ABC = 60/3 = 30

    thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,

    AC=24/√3=8√3AL bisects angle A = >m∠LAC=30

    ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16
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