Question

In a right angled triangle ,the difference between two acute angles is π/9 radians .find the angle in degrees

Answer 1

$let \: \:one \: \: of \: \: the \: \: acute \: \: angle \: \: be \: \: x \\ then \: \: other \: \: angle \: \: is \: \:x - \frac{\pi}{9} \\ \\ since \: \: it \: \: is \: \: right \: \: angled \\ sum \: \: of \: \: acute \: \: angles \: \: is \: \: \frac{\pi}{2} \\ \\ thus \: \: x + (x - \frac{\pi}{9} ) = \frac{\pi}{2} \\ 2x = \frac{\pi}{2} + \frac{\pi}{9} \\ x = \frac{11\pi}{36} \\ \\ therefore \: \: in \: \: degrees \\ one \: \: acute \: \: angle = \frac{11\pi}{36} \times \frac{180}{\pi} = 55 \\ other \: \: angle = 90 - 55 = 35$