Express answer in exact form. show all work for full credit. a segment of a circle has a 120 degree arc and a chord of 8 sqrt 3 in. find the area of the segment.

( approx )

Step-by-step explanation:

Let r be the radius ( in inches ) of the circle,

Given,

The length of the chord is 8√3 inches,

By making the diagram,

We found there is a triangle having sides r, r and 8√3,

Also, having angle 120° opposite to sides measuring 8√3 inches,

By the law of cosine,

Now, area of a segment by an degree arc is,

Where, x is the radius of the circle.

Hence, the area of the segment having 120 degree arc on a circle with radius 8 inches,

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step-by-step explanati∵∵∴∴on:

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58