Question

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

Answer 1

`r= (AB)/(2) \\ \\A_(semi\:circle )=(r^2\pi)/(2) \\ \\A_(triangle)=A_(semi\:circle )=(r^2\pi)/(2) \\ \\A_(triangle)= (2r* h)/(2) =rh \\ \\(r^2\pi)/(2)= rh \\ \\h=(r\pi)/(2) \\ \\ tan(x)= (h)/(r) = ((r\pi)/(2))/(r) =(\pi)/(2) \\ \\x=\arctan{(\pi)/(2)} \\ \\x \approx 57.52^o`