Question

Find the area of a sector with an arc length of 60 in. and a radius of 15 in.




A.

117.75 in.²


B.

282.60 in.²


C.

450 in.²


D.

6,750 in.²
HELPPPPP!!!!!

Answer 1

l = theta/360 * 2Pi * r
60 = theta/360 * 2Pi * 15

theta/360 = 2/Pi

theta = 720/Pi

Area = theta/360 * Pi r^2

Area = 720/Pi * 1/360 * Pi 15^2

Area = 2*225 = 450 ins^2
When angle is in radians, you can say any of the following:
{key: L = arc Length, ϴ = central angle, r = radius, A = sector area}

L = rϴ
A = ½r²ϴ
or, combining the two above equations, we get a third gem:
A = ½rL <--- this is the one we're going to use

A = ½rL
A = ½*60*15 = 450 in² [C]

Answer 2

first step, we have to find the subsequent angle \(\alpha\):