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.

Answer 1

this is the problem i will give medals to whoever gets it right

Answer 2

Is this what you mean and you have to find the area enclosed by the arc and the chord?

@whizkidzack

Answer 3

it should have like a explanation and pictures on the attachment

Answer 4

What the question is asking is basically the area enclosed by arc AB.

Answer 5

We are basically finding the area of the space enclosed by the arc AB and segment AB.

To do this, we must first find the area of the 120 degrees portion of the circle. Enclosed by arc AB and radii AC and CB. After finding that area, we must then find the area of the isoceles triangle (it's isosceles because the two sides of the triangles are the radii of the circle thus the same). We can use the sine law (you could also use cosine law) to find the sides of the triangle and we can then find the area of the triangle by either using heron's formula (which you might not know), or drawing a perpendicular line from point C to the base of the triangle and using trig ratios to find the ratio of the triangle and using the (base x height) / 2 formula. After we know the area of the triangle, we subtract this triangle area of the area of the 120 degree portion of the circle and that gives us the area enclosed by arc subtended by the chord AB.

Do you understand? And do you know how you would do that? I've outlined the steps you need to take to find the area and if you know all that, then it should be easy. If you want though, I can literally take you through the process of how it could be done.

@whizkidzack

Answer 6

whats herons formula

Answer 7

Heron's formula is a formula for finding the area of a triangle when you know the lengths of all three sides. You don't need to know it for this question but you could use it to solve this if you wanted to.

Answer 8

ok h

Answer 9

ok how do you do it

Answer 10

Ok, think of it like this:
You get what I mean now?

@whizkidzack