Finding specific sectors
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Finding specific sectors

[From: ] [author: ] [Date: 11-08-13] [Hit: ]
Then i subtract the sector area from the triangle area of both circles, i add the result to get the shaded area alone. This however doesnt work all that well.http://imageshack.us/photo/my-images/88/wolframalpha20110812155.The heights are found first by drawing an angle bisector from angle PAQ.......
The problem is in this link:

http://imageshack.us/photo/my-images/26/capturetfb.jpg/

The goal is to find the shaded area. First i go about finding the height of both triangles (APQ and BQP). Then i find areas both sectors. Then i subtract the sector area from the triangle area of both circles, i add the result to get the shaded area alone. This however doesn't work all that well. Here's my calculation:

http://imageshack.us/photo/my-images/88/wolframalpha20110812155.gif/

The heights are found first by drawing an angle bisector from angle PAQ. Since it's an isosceles triangle, it divides PQ in half. Thus the height is 7^2+h^2=25^2. Same procedure for the other triangle.

What is wrong?

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You have used the same value for the angle at B as the angle at A. Wrong !

sin(B/2) = 7 / (35/3) = 0.6

B/2 = 36.87°, therefore B = 73.74°

Use that instead of 32.5° for B. That should do it.
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