Find the Area of a segment of a circle if the central angle of the segment is 105 ∘ degrees and the radius is 70.

Question

Find the Area of a segment of a circle if the central angle of the segment is       105    ∘   degrees and the radius is   70.

Tristin Case · Accepted 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} θ

if

θ

is in radians or

\frac{1}{2} r^{2} π \frac{θ}{180^{\circ}}

if

θ

is in degrees.
The area of the triangle is give by

\frac{1}{2} r^{2} \sin θ

.
Combining these two gives:

\frac{1}{2} \times 70^{2} \times π \times \frac{105^{\circ}}{180^{\circ}} - \frac{1}{2} \times 70^{2} \times \sin 105^{\circ} \approx 2123.34

skynugurq7 · Accepted Answer

Formulas that you need to know:(1) The area formula for   △  A  B  C   [  A  =            1      2        a  b  sin  ⁡  C  ].(2) The area of a sector (OAB) formula   [  A  =            1      2            r    2    θ  ]; where   θ is the central angle and it should be in radian instead of degree.Added. The conversion formula is [  [  π radians   =      180    0    ].

Find the Area of a segment of a circle if

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