Question

A piece of land is in the shape of a sector. Its area is 900 sq ft, while its arc length is 30 ft. What is the measure of the angle between the two radii of the sector?

Answer 1

C= 2 radians.

Explanation

Length of arc = r C where r = the radius and C is the angle in radians.

Area of the sector = 1/2 r^2 C

So we have:

30 = rC and

900 = 1/2 r^2 C

From the first equation we have r = 30/C so substituting for r:

900 = 1/2 (30/C)^2 * C

900 = 0.50 (900/C^2) * C

900 = 450/C

C= 2 radians.