What is the approximate area of a segment of a circle with a radius 12 meters if the length of the chord is 20 meters? Round your answer to the nearest whole number.

I started but i could not solve for theta given as:

20=24sin(theta/2)

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- Mar 19th 2008, 05:47 PMhamadouousmanevery confusing homework
What is the approximate area of a segment of a circle with a radius 12 meters if the length of the chord is 20 meters? Round your answer to the nearest whole number.

I started but i could not solve for theta given as:

20=24sin(theta/2) - Mar 19th 2008, 06:16 PMtopher0805
$\displaystyle 20 = 24sin\left(\frac {\theta}{2}\right)$

$\displaystyle sin\left(\frac {\theta}{2}\right) = \frac {5}{6}$

Where did you get that formula from? - Mar 19th 2008, 06:34 PMtopher0805
http://img208.imageshack.us/img208/8541/segmentmm8.jpg

Notice that I have divide the isosceles triangle in half, creating two right angle triangles. We know that the hypotenuse is 12 and that one side is 10 so all we have to do is find the angle we need and multiply it by 2.

So we have:

$\displaystyle \sin {\theta} = \frac {10}{12}$

$\displaystyle \sin {\theta} = \frac {5}{6}$

Use the arcsin function to solve for $\displaystyle \theta$ and then plug that into this formula:

$\displaystyle \frac {1}{2}r^2\left(\frac {\pi}{180}\theta - \sin {\theta}\right)$ If you are using degrees

or

$\displaystyle \frac {1}{2}r^2\left(\theta - \sin {\theta}\right)$ If you are using radians.