Let the radius of the circle be r and let the perpendicular height of the triangle be h.

tan x ° = h / r

Now, the area of the semicircle =

\frac{1}{2} π r^{2}

and the area of the triangle =

\frac{1}{2} \times 2 r \times h

Which gives $r h$ = $\frac{1}{2} π r^{2}$ , so $\frac{h}{r} = \frac{π}{2}$

Solution