Find the Area of a segment of a circle if the central angle of the segment is $105^\circ$ degrees and the radius is $70$.
Formulas I have:
- Area of a non-right angle triangle= $\frac{1}{2}a b \sin C$.
- Area of segment = ( area of sector ) $-$ (area of triangle).
Please, could you explain it step by step so I can understand, thanks
Best Answer
You can work out the area of the sector then subtract the area of the triangle.
The area of a sector is given by $\frac{1}{2}r^2\theta$ if $\theta$ is in radians or $\frac{1}{2}r^2\pi\frac{\theta}{180^\circ}$ if $\theta$ is in degrees.
The area of the triangle is give by $\frac{1}{2}r^2\sin\theta$.
Combining these two gives: $\frac{1}{2}\times70^2\times\pi\times\frac{105^\circ}{180^\circ}-\frac{1}{2}\times70^2\times\sin105^\circ \approx 2123.34$