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).

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