Question

The semi circle and isosceles triangle have the same base AB and the same area. Find angle x. Show workout.

Answer 1

$r= \frac{AB}{2} \\ \\A_{semi\:circle }=\frac{r^2\pi}{2} \\ \\A_{triangle}=A_{semi\:circle }=\frac{r^2\pi}{2} \\ \\A_{triangle}= \frac{2r\times h}{2} =rh \\ \\\frac{r^2\pi}{2}= rh \\ \\h=\frac{r\pi}{2} \\ \\ \tan{x}= \frac{h}{r} = \frac{\frac{r\pi}{2}}{r} =\frac{\pi}{2} \\ \\x=\arctan{\frac{\pi}{2}} \\ \\x \approx 57.52^o$