Question

C is the center of the semicircle as shown in the above figure. If the area of the semicircle is $8\pi$, find the area of triangle $ABC$ in terms of $\theta$.

• A. $2\sin \theta \tan \theta$
• B. $4\sin \theta$
• C. $8\cos \theta$
• D. $8\sin \theta$
• E. $8\sin \theta \tan \theta$

Answer 1

The correct option is D $8\sin \theta$

Area of semicircle is $\frac{\pi r^2}{2}=8\pi$

$\Rightarrow r=4=CB=CA$
Area of triangle $ABC$ $=\frac{1}{2}\times CA\times CB\times \sin \theta$

$=\frac{1}{2}\times 16\times \sin \theta$

$=8\sin \theta$