SOLUTION: what is the approximate area of a segment of a circle with a radius 12m if the length of the chord is 20m?

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Question 75245: what is the approximate area of a segment of a circle with a radius 12m if the length of the chord is 20m?
Answer by zerosignal(28) About Me  (Show Source):
You can put this solution on YOUR website!
Formula for a segment of a circle is a+=+%281%2F2%29%2A%28%28r%2AL%29-c%28r-h%29%29
given: r =12, c = 20
First, we must find "h" & "L"
To find "h":
h+=+r-%281%2F2%29%2Asqrt%28%28%284%29%2Ar%5E2%29-c%5E2%29
h+=+12-%281%2F2%29%2Asqrt%28%284%2A12%5E2%29-%2820%5E2%29%29
h+=+12-%281%2F2%29%2Asqrt%28576-400%29
h+=+12-%281%2F2%29%2Asqrt%28176%29
h+=+12-%281%2F2%29%2A%2813.26649916%29
h+=+12-%286.633249581%29
h+=+5.366750419
Next, find "L":
L+=+0.01745%2Ar%2Aangle
we dont know the angle yet, so solve for the angle first:
SinX+=+%2810%2F12%29
SinX+=+.833333333
Sin%5E-1%28.833333333%29+=+X
56.44269024+=+X
multiply by 2 to get total angle;
56.44269024%2A2+=+112.8853805
now solve for "L":
L+=+0.01745%2Ar%2Aangle
L+=+0.01745%2A12%2A112.8853805
L+=+23.63819867
Now solve for area:
a+=+%281%2F2%29%2A%28%28r%2AL%29-c%28r-h%29%29
a+=+%281%2F2%29%2A%28%2812%2A23.63819867%29-20%2812-5.366750419%29%29
a+=+%281%2F2%29%2A%28%28283.658384%29-20%286.633249581%29%29
a+=+%281%2F2%29%2A%28%28283.658384%29-%28132.6649916%29%29
a+=+%281%2F2%29%2A%28150.9933924%29
a+=+75.4966962
so the approximate area is 75.5m