A circle with the radius of 6 in. is placed on a triangle. How do i find the area of the space that the circle doesn't take up?? of, and the radius makes a 90 degree angle with the triangle.

Question

owlfred · Answer

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anonymous · Answer

So you have a triangle with a circle inside it where they intersect at exactly 3 points?

anonymous · Answer

yup.

anonymous · Answer

Just working through a little geometry here, but it seems to me that we have something like this:

anonymous · Answer

yeah... i think the lines at the top were added in, but thats pretty much what it looks like.

anonymous · Answer

So that being the case..
If we let x be the length of the hypotenuse of that right triangle, then:

$$x = {6 \over sin\ 30^\circ}$$$$Base = x(cos\ 30^\circ) = 6(tan\ 30^\circ)$$$$Height = x + 6 = 6({1 \over sin\ 30^\circ} + 1) $$

anonymous · Answer

Whoops. The base should be 2 times x(cos 30)

anonymous · Answer

So 12(tan 30)

anonymous · Answer

why use trig? we are learning about sectors.... im just wondering a bit.

anonymous · Answer

Oh, I used trig cause it made the most sense to me. If you know of another way to solve it, feel free.

anonymous · Answer

oh ok. thanks!!

anonymous · Answer

I just found the base and height, then can use that to find the area of the triangle. Then I can subtract the area of the circle from that to find the space the circle doesn't occupy.

anonymous · Answer

i really appreciate your help.... my teacher is didn't show us how to do this kind of problem. and that makes a lot of sense now. thanks!!