Question

Express answer in exact form.

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

Answer 1

Not sure if the drawing helps. Anyway, trace your chord on the circle, and join the endpoints of the chord with the center of the circle (tracing 2 radii). Now, trace a perpendicular line from the center to the chord.

You have now created 2 right triangles, with base = 4'', and hypotenuse = 8''. You will need to find the angle alpha using
\[\sin(\alpha)=opposite/hypotenuse\]

Now you know that double the angle alpha creates that arc segment on the circle...so...
If the whole circle, that is, a whole 2*pi angle creates a circumference of 2*pi*radius, then what circumference does this angle that you calculated create?