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

Let be the angle of an arc,   and r be the radius of the circle.

Then by the cosine rule,

1. Find the area of the sector. Since then

2. Find the area of the triangle formed by two radii and chord:

3. The area of the segment is

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!