Question

Find the measure of AC, given that the shaded region has an area of 45.55 square centimeters. Use your calculator and round your final answer to two decimal places.

Answer 1

First, you need to find the angle at B. To do this, calculate the area of the circle, which is r²pi, in your case

6*6*pi

Now, the angle at B is the ratio of the two areas times 360°:

360° * 45.55 / (6*6*pi)

To get the distance from A to C (I assume this is what you want), there are at least two possibilities:
a) there is a formula (a sort of generalized Pythagoras) where you can find the side in a triangle opposite to some angle (it uses the cosine).
b) you can observe that the triangle ABC is isosceles; so you can halve the angle at B and by this draw a line from B perpendicularly to AC. Then, by using simple cosine, you can compute the length of AC/2 from the angle and the 6cm.

Answer 2

does this help?

Answer 3

360° * 45.55 / (6*6*pi)

Answer 4

πr² = 36π.

Now, find out what fraction of the circle that the sector takes up.

45.55 / 36π ≈ 0.428

Now, multiply the circumference of the circle by that value and you have the answer.

The circumference is 2πr = 12π.

12π times 0.428 = 15.18 cm
IS THIS CORRECT?

Answer 5

yes