Question

Express answer in exact form.

Find the area of the larger segment whose chord is 8" long in a circle with an 8" radius.

Answer 1

none has answered to this 1 yet????? O.o

Answer 2

nope

Answer 3

ask Amistre

Answer 4

Firstly, find the area of the sector that would fit that segment. Between the chord, and the two radii, you get an equilateral triangle with sides of length 8". That means the internal angle is 60\(^o\), or \(\frac{\pi}{3}\) radians. The area of the sector is given by:\[area=\frac{\pi r^2}{angle \: \: in \: \: radians}\]\[area=\frac{\pi (8)^2}{\pi /3}=192\] The area of the triangle is given by \(\frac{1}{2}base \times height\). The base is 8", and you can find the height using trigonometric rules, or Pythagora's Theorem. The difference between these two areas is the area of the segment.