Question

If ${\sin }^{-1}\frac{5}{x}+{\sin }^{-1}\frac{12}{x}=\frac{\pi }{2}$, then find value of $x$.

Answer 1

Answer: 13.00

${\cos }^{-1}\frac{\sqrt{x^2-25}}{x}+{\sin }^{-1}\frac{12}{x}=\frac{\pi }{2}$
$\sqrt{x^2-25}=12$
$x^2=169$
$x=13$