Finding Area of a triangle inside a semi circle.

Question

I'm familiar with basic high school trig. The answer is $2\sin(\theta)\cos(\theta)$. I'd appreciate it if someone could give me an explanation.

Answer 1

Hint. That triangle is actually a right triangle. The solution easily follows. Can you explain it?

Answer 2

Notice, the angle subtended by the diameter at any point on the circumference of a semicircle is a right angle hence the triangle is a right triangle.

in the right triangle, the hypotenuse (i.e. the diameter of circle) is $2$ & the legs (base & perpendicular ) can be easily calculated using Pythagorus theorem as $2\sin\theta$ & $2\cos \theta$

hence the area of the right triangle is given as $$=\frac{1}{2}(\text{base})(\text{perpendicular})=\frac{1}{2}(2\sin\theta)(2\cos\theta)=2\sin\theta\cos\theta$$