Express answer in exact form.

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

Question

Express answer in exact form.

A segment of a circle has a 120 degree arc and a chord of 8 square root of three in. Find the area of the segment.

anonymous · Answer

A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.


      
$$A=(\frac{ aa}{ b }\pi - \sqrt[aa]{b}$$

anonymous · Answer

the double a means there are two numbers there

anonymous · Answer

inches squared at the end of the diagram

terenzreignz · Answer

A radius would be nice.

anonymous · Answer

it doesnt give me one

terenzreignz · Answer

It gives you enough info to get the radius though... 
The arclength L with a given angle A is given by
$$\huge L = \frac{A}{360^o}\times2\pi r$$

anonymous · Answer

so it would be 120/360*2pi

terenzreignz · Answer

A = 120 degress...
and 
L = ?

anonymous · Answer

L= 
$$8\sqrt{3}$$

terenzreignz · Answer

good.  So..
$$\huge 8\sqrt3=\frac{120^o}{360^o}\times2\pi r$$
And now, just solve for r.

anonymous · Answer

i got 2.1

terenzreignz · Answer

hmm... best not to approximate  yet, keep the pi, keep the radical.  Do the approximating at the end, with the final answer.

anonymous · Answer

im so confused