A circle has a chord that goes from #( 3 pi)/8 # to #(4 pi) / 3 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?
1 Answer
Explanation:
To start, we know that the area of a circle is equal it the radius square times pi.
We also know the area of the circle is
We can divide through by pi.
And square root.
We have calculated the radius of the circle.
Now to find the angle across our chord we subtract the two angles we have been given.
From the image we can see the angle has been bisected, also bisecting the chord creating two right-angled triangles.
Using trigonometry we can calculate half the length of the chord.
We have the radius/hypotenuse, the angle
This is the length of half the chord, so the chord length is