In a right angled triangle, the hypotenuse is four times the perpendicular drawn to it from the opposite vertex. The value of one of the acute angles is
Let the legs be \(a, b\), the hypotenuse \(c\), and the altitude to the hypotenuse \(h = \frac{ab}{c}\).
Given \(c = 4h\): \(ab = \frac{c^2}{4}\).
With \(a = c\sin A\) and \(b = c\cos A\): \(c^2\sin A\cos A = \frac{c^2}{4}\), so \(\sin 2A = \frac{1}{2}\).
\(2A = 30°\), so \(A = 15°\) (the other acute angle is 75°).
Answer: (C) 15°
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