Problema Solution
A stake is located 10.8 feet from the end of a closed gate that is 8 feet long. The gate swings open, and it's end hits the stake. Through what angle does the gate swing
Answer provided by our tutors
the gate is forming a circle of radius 8 feet and swing through a distance that creates a chord of lengt
h 10.8 feet... let 'a' represent the angle through which the gate swings:
chord length = 2*r(sin(a/2))
10.8 = 2*8(sin(a/2))
0.675 = sin(a/2)
a/2 = arcsin(0.675)
a = 2*arcsin(0.675)
solving for 'a' we have a=84.9
the door swings through an arc of 84.9 degrees