In a right angled Δle, the hypotenuse is 22 times the length of perpendicular drawn from the opposite vertex to the hypotenuse, then the other two angles are - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

$\tan A = \frac{x}{A M} \Rightarrow A M = \frac{x}{\tan A}$

Similarly $C M = \frac{x}{\tan C}$

$A M + C M = 2 \sqrt{2} x$

$2 \sqrt{2} x = \frac{x}{\tan A} + \frac{x}{\tan C}$

$2 \sqrt{2} = \frac{1}{\tan A} + \frac{1}{\tan C}$

$\tan A + \tan C = 2 \sqrt{2} \tan A \tan C$

Also $A + C = \frac{π}{2}$

$\frac{\tan A + \tan C}{1 - \tan A \tan C} = \infty$

$\tan A \tan C = 1$

$\tan A + \tan C = 2 \sqrt{2}$

$\tan A \tan C = 1$

By solving these two we get $\tan A = \sqrt{2} + 1$

$\tan C = \sqrt{2} - 1$

In a right angled $Δ^{l e}$ , the hypotenuse is $2 \sqrt{2}$ times the length of perpendicular drawn from the opposite vertex to the hypotenuse, then the other two angles are