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

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

Respuesta :

[tex]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[/tex]