The length of the arc contracted by the chord is 30 pi cm, and the angle formed by this chord and the radius drawn through its

The length of the arc contracted by the chord is 30 pi cm, and the angle formed by this chord and the radius drawn through its end is 15 degrees. Find the area of the sector bounded by this arc.

Let us draw from point O the radii of the circle OA and OB.

Then ОА = ОВ = R, which means that the triangle ОАВ is isosceles with the base AB, which means that the angle AOB = OBA = 150, then the angle AOB = (180 – 15 – 15) = 150.

Knowing the length of the arc AB, we determine the radius of the circle.

L = π * R * AOB / 180.

R = 180 * L / π * AOB = 180 * π * 30 / π * 150 = 36 cm.

Let us determine the area of the sector bounded by the arc AB.

S = π * R2 * AOB / 360 = π * 1296 * 150/360 = 540 * π cm2.

Answer: The area of the sector is 540 * π cm2.