Question

In a right angled triangle the hypotenuse is $2\sqrt{2}$ times the length of perpendicular drawn from the opposite vertex on the hypotenuse, then the other two angles are ______.

Answer 1

AB$=$AD$+$BD
$2\sqrt{2}p=p\cot A+p\cot ({90}^o-A)$
or $2\sqrt{2}=\cot A+\tan A$
or $2\sqrt{2}=\frac{1}{\sin A\cos A}$
or $\sin 2A=\frac{1}{\sqrt{2}}=\sin \frac{\pi }{4}$
$\therefore A=\frac{\pi }{8},B=\frac{\pi }{2}-A=\frac{\pi }{2}-\frac{\pi }{8}=\frac{3\pi }{8}$.