SOLUTION: A builder intends placing 7 equally spaced homes on a semicircular plot as shown in the accompanying figure. If the circle has a diameter of 400 feet, what is the distance between

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Question 1046085: A builder intends placing 7 equally spaced homes on a semicircular plot as shown in the accompanying figure. If the circle has a diameter of 400 feet, what is the distance between any two adjacent homes?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Central angle is 360%2F7=51.42857=%2851%263%2F7%29degrees.

radius of the circle is 200feet.

Triangle formed is isosceles, and you could use Law Of Cosines to find the distance between any two nearest houses around the circle. You could also split the triangle into two right-triangles sharing a radius as the longest common leg.


If choosing Law Of Cosines:
200%5E2%2B200%5E2-2%2A200%2A200%2Acos%2851%263%2F7%29=d%5E2, simplify and solve for d.


MISTAKE: I answered the wrong problem for you. Your description said, "semicircle"; and by mistake, I solved for "circle". Actual central angle will be 180%2F7 degrees.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Double mistake.

The central angle is 180%2F%287-1%29 = 180%2F6 = 30 degrees.