# Find the Area of a segment of a circle if

Find the Area of a segment of a circle if the central angle of the segment is ${105}^{\circ }$ degrees and the radius is $70$.
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Tristin Case
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 $\frac{1}{2}{r}^{2}\mathrm{sin}\theta$.
Combining these two gives: $\frac{1}{2}×{70}^{2}×\pi ×\frac{{105}^{\circ }}{{180}^{\circ }}-\frac{1}{2}×{70}^{2}×\mathrm{sin}{105}^{\circ }\approx 2123.34$
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skynugurq7
Formulas that you need to know:
(1) The area formula for $\mathrm{△}ABC$ $\left[A=\frac{1}{2}ab\mathrm{sin}C\right]$.
(2) The area of a sector (OAB) formula $\left[A=\frac{1}{2}{r}^{2}\theta \right]$; where $\theta$ is the central angle and it should be in radian instead of degree.Added. The conversion formula is [$\left[\pi$ radians $={180}^{0}\right]$.