Question

An 8-inch dinner knife is sitting on a circular plate so that its ends are on the edge of the plate. If the minor arc that is intercepted by the knife measures 120 degrees, find the length of the diameter of the plate. Round your final answer to two decimal places.

Answer 1

The diameter of the plate is 9.24 inches

Step-by-step explanation:

Let us consider the radius to be 'r'

Angle = 120°

Chord length = 8 inches

Chord length = 2rsin(θ/2)

8 = 2r sin(120/2)

8 = 2r sin60°

8/2 = r (√3/2)

4/(√3/2) = r

r = 8/√3

r = 8/1.73

r = 4.62 inches

Diameter of the plate = 2(4.62)

= 9.24 inches

The diameter of the plate is 9.24 inches