# Math

posted by Prince

1. Find the area of a segment of height 22.1 inches in a circle of radius 6.42 ft. Draw a rough sketch of a circle showing the height and radius. Consider significant digits.

1. Reiny

the perpendicalar to the chord will be 22.1 inches
and it will meet the chord at its midpoint
So you have a rightangled triangle with the radius as the hypotenuse 6.42 ft or 77.04 inches
and shorter sides 22.1 and x
Use Pythagoras to find the radius

x^2 + 22.1^2 = 77.04^2

-use basic trig to find the central angle of the sector
-use a ration to find the area of the sector
-find the area of the triangle formed by the chord and the centre of the circle, you know the angle

Area of whole circle = 70.04^2 π

subtract the area of the triangle from the area of the sector to find the area of the segment.

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