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23 February, 04:25

Prove that, in a right triangle with a 15° angle, the altitude to the hypotenuse is one fourth of the hypotenuse (without using trigonometric functions).

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  1. 23 February, 06:15
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    a = b/4

    Step-by-step explanation:

    Let a be the altitude to the hypotenuse and b be the hypotenuse. The 15° angle faces a and the right angle faces b.

    Using the sine rule,

    a/sin15 = b/sin90

    a = bsin15/sin90

    = 0.25b

    = 25b/100

    = b/4
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