Algebra

In △ABC, m∠ACB=90°, m∠ACD=60°,
CD
is the altitude to
AB
, and BD = 5 cm. Find AD.

(A) 6cm (B) 15cm (C) 20cm (D) 25cm

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  1. After you make your sketch, you will realize that your are dealing
    with 3 similar triangles with angles 30°, 60°, 90°
    with corresponding sides in the ratio of 1 : √3 : 2
    So should be easy to see with simple ratios that CD = 5√3 and x = 15

    or, ..... you could just use basic trig
    In triangle BCD, tan60° = CD/5
    √3 = CD/5
    CD = 3√5 , as above
    Now in triangle ADC, tan60° = x/CD
    x = CDtan60°
    = (3√5)(√3) = 15 , as above

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    Reiny

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