Question

Suppose XZ¯¯¯¯¯¯ is drawn in the circle below. What is the area bounded by arc XZ and XZ¯¯¯¯¯¯ to the nearest tenth?

http://tinypic.com/r/bjajid/8
This is the graph

Answer 1

Multiply angle degree to radius and convert to radians? @amistre64

Answer 2

area of pizza slice - area of triangle is area of sector

how do we find that area of the slice? to start with

Answer 3

I have to go right now \(\huge\ddot\frown\)

Answer 4

no need to convert to rads; 120 out of 360 is the ratio

Answer 5

"Good luck"

Answer 6

is the answer 15.6?

Answer 7

dunno, we havent gotten to the end of it

Answer 8

I am lost can you explain?

Answer 9

do you agree that the area associated with a circle and its angle is:

360 degrees :to: pi r^2

??

Answer 10

yes that makes sense

Answer 11

then we simply need to multiply each side by the same amount to keep the ratio equal

360 * 120/360 = 120 sooo lets do that since we want 120 degrees and its area

120 degrees :to: 12/36 pi r^2 is the area of the pizza shaped part.

Answer 12

Area of slice = 1/3 pi (6)^2

agreed?

Answer 13

okay yes that is 37?

Answer 14

now, if we draw a line, and make the triangle, we need to subtract the area of the triangle from this 12pi value

12pi - (triangle area) = (area of desired)

Answer 15

what are your ideas on how to find the height and width of this triangle to determine its area?

Answer 16

6 is the base and the height is 4.25

Answer 17

let draw it in a more normal orientation

Answer 18

we can use trig functions to determine h and b ...

Answer 19

which trig function deals with : over/hyp?

which trig function deals with : adj/hyp?

Answer 20

I have no idea honestly

Answer 21

im sorry can you give me the answer so i dont get timed out then explain?

Answer 22

you should have material that defines the trig function. sin, cos, and tan. can you find them for me?

Answer 23

no, this is a teaching site, not an answering service. its best to be used before tkaing any timed events because the quality of teaching tends to be time extensive.

Answer 24

but we are almost done .... as long as we can find the trig function definitions, we can choose which ones to apply

Answer 25

another option would be something called 'special trangles' if that is material you have covered? it may be simpler

Answer 26

hmmm i dont beleve i have covered either?

Answer 27

hmm, then they should have not given this question :) it requires on or the other.

lets do special triangle

if we take an equilateral triangle, and split it in half, we get the special 30-60-90 degrees the we seek