Question

Express answer in exact form. Show all work for full credit.
A segment of a circle has a 120 arc and a chord of 8sqrt 3in. Find the area of the segment.
Can someone please help me with this? I'm literally about to have a mental breakdown.

Answer 1

@Vocaloid

Answer 2

She can help explain everything to you

Answer 3

Thank you...

Answer 4

Any chance you could screenshot your question? It might make it a little easier for us to understand.

Answer 5

http://prntscr.com/hhwmma

Answer 6

the area of the shaded part is the area of the entire sector - the area of the triangular part

Answer 7

to find the area of the triangular part we will bisect the chord to produce two 30-60-90 triangles

Answer 8

given that the entire chord is \[8\sqrt{3}\] the half chord is \[4\sqrt{3}\]

Answer 9

using our 30-6-90 triangle ratios we get

Answer 10

now we know: the height of each triangle, the base of each triangle, and the radius of the circle. these three pieces are enough to calculate the area using our original equation

area shaded = area sector - area of triangles

for a sector, the area is (angle of sector/360)*pi*r^2
area of each triangle is (1/2)(bh)

r = 8
angle of sector = 120
b = 4sqrt(3)
h = 4

let me know if you had any trouble understanding anything

Answer 11

Thank you so much... You did make it easier to understand.. I had my answer right, my teacher just wanted it in a different format I guess. :)