Express answer in exact form.
a segment of a circle has a 120 arc and a chord of 8√3 in. find the area of the segment.

show work i am totally stuck on this.. you (75 points)

Step-by-step explanation:

Area of segment equals area of sector minus area of isosceles triangle.

Given; the length of chord,

and the angle of the sector, .

We can use the formula for calculating the length of a chord to find the radius of the circle.

Area of segment

The  area of segment = 39.34 square unit

Step-by-step explanation:

From the figure attached with this shows the pictorial representation.

From this we can see that shaded region, which is a segment. We have to calculate the ea of segment.

To find the radius of circle

In triangle OAC ,have angles 30°, 60° and 90°

OC : AC : OA = 1 : √3 : 2

AC = 8√3/2 = 4√3

Then, OC = 4 and OA = 8

Radius of circle r = 8

To find the area of sector

Area of sector = (120/360)*πr²

 = 1/3 * 22/7 * 8 * 8 = 67.05 square units.

To find area of triangle ABO

Area = 1/2(base*height)  = 1/2(AB * OC)

Area = 1/2 * 8√3 * 4 = 16√3= 27. 71 square units

To find area of segment

Area of segment = Area of sector - Area of triangle

= 67.05 - 27.71 = 39.34 square unit

Therefore area of segment = 39.34 square unit

step-by-step explanation:

1

step-by-step explanation:

it's the only multiple of both and the least