Finding angle in triangle and semicircle

[jacky50]

Dear all,
right now, I am doing my IGCSE and this question is in my coursebook. I can't think of any way to calculate it...
It's part of the section circumference and area of circles. So must be some how solved using this.

The semi-circle and the isosceles triangle have the same base AB and the same area. Find the angle x.
The answer is: 57.5°

Thanks a lot in advance
Jacky

 

[tiny-tim]

Welcome to PF!

Hi Jacky! Welcome to PF!

Call the angle x, and the length AB 1 …

what are the areas of the triangle and the circle?

 

[jacky50]

Hey tiny-tim, thanks :)

the area is not given, just that its the same

 

[tiny-tim]

I know they're not given …

I'm asking you what they are

 

[jacky50]

Area of semi-circle = 0.5 x pi x (0.5AB)^2
But I don't have a clue about the triangle

 

[tiny-tim]

But I don't have a clue about the triangle

Split it into two right-angled triangles.