A circle has a radius of 9 cm and a sector of the circle has an arc length of 9.7 cm. The angle at the centre of the sector is X°.Calculate the value of x to the nearest degree.

Accepted Solution

Answer:The value of X is 62 degreesStep-by-step explanation:The arc length L  of a circle is given by formula:L= 2(pi)(r)X / 360 (1)where pi = 3.14, r is the radius of the circle and X the angle that produces the arc. You want the angle X so we can simplify X in equation (1) 360L=2(pi)(r)X360L/2(pi)(r)= XX =  360L/2(pi)(r)We replace the radius r=9cm the arc L = 9.7 cm and pi and obtain X = 360* (9.7 cm)/ 2(3.14)*(9cm) = 3492/56.52 = 61.78 That rounded to nearest degree is 62 degrees.