Question

Find the length of a chord intercepted by a central angle of 25 degrees in a circle of radius 30 feet

Answer 1

let the length of the chord be 2x ft
Drop a perpendicular from the central vertex to the chord
then sin 12.5 = x/30
x = 30sin12.5
2x = 60sin12.5 = 12.9864

or by cosine law:
let the length of the chord be c
c^2 = 30^2 + 30^2 - 2(30)(30)cos25
= 168.64598..
c = 12.9864 , same as above