Question

Express answer in exact form.

A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.

Answer 1

what are the units for that 120 arc?

Answer 2

Oh sorry! 120 degrees, and 8 sqrt 3 inches. My bad!

Answer 3

So you have a circle with center 0, and a chord from point P to point Q on the circle, measuring m inches.

PQ0 is a triangle with angle 120 degrees, if you draw a line splitting it in half, you have a 90 degree angle, a 60 degree angle, and a length m/2 inches.

For this we see the equation, r*sin(theta) = m/2, or more specifically, r * sin(60) = m/2.

From here you should be able to compute the area.

Answer 4

(8sqrt3)^2=r^2 + r^2 -2(r)(r)cos120
r^2 can be found
area can be calculated by
(r^2) pi (120/360)