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?

Question

Mathematics

Jasper Tucker

29 March, 16:59

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?

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Answers (1)

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Dwayne Kramer · Answer 1

C = 2 radians.

Step-by-step 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.