The inscribed angle of a circle with a length of 36 p cm is 35 degrees. Find:

The inscribed angle of a circle with a length of 36 p cm is 35 degrees. Find: a) the length of the arc on which this angle rests; b) the area of the sector bounded by this arc.

a) The length of the arc on which the angle rests is proportional to that angle. We make a proportion according to which an angle of 360 ° corresponds to a circumference of 36 * n cm, and an angle of 35 ° – x cm:

360 ° / (36 * n) = 35 ° / x;

x = (36 * n * 35 °) / 360 ° = (35 ° * n) / 10 = 3.5p cm.

Answer: 3.5p cm.

b) Find the radius of the circle:

L = 2nR;

R = L / 2p = 36p / 2p = 18 cm.

Area of a circle: S = nR ^ 2 = n * 18 ^ 2 cm ^ 2.

The area s enclosed in a sector is proportional to the angle a that bounds it.

s = (S * a) / 360 °.

s = (n * 18 ^ 2 * 35 °) / 360 ° = (n * 18 * 35) / 20 = (n * 9 * 7) / 2 = 31.5n cm ^ 2.

Answer: 31.5n cm ^ 2.