Karen is looking at the edge of a large circular object from a distance. From her view, the object appears as a line segment. She knows that the distances between herself and the points on the edges of what appears to be a line segment measure 25 feet. She also knows from her location, the edges form an angle at the point she is standing at that measures 45Β°. Find the diameter of the object that Karen is looking at.

Accepted Solution

d = 25 ft Ο‰ = (45ΒΊ) ⁄ 2 = 22.5ΒΊ sin(Ο‰) = R ⁄ d                 sin(22.5ΒΊ) = R ⁄ 25                 R = 9.57 feet Diameter = 2R Diameter = 2 β€’ (9.57) Diameter = 19.1 feet Diameter = 19 feet (when rounded)