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°, find the diameter of the plate. show all work.

Answer 1

When we form a right triangle connecting the edge of the knife to the center of the circle and the center of the knife to the center of the circle, the radius of the circle becomes the hypotenuse. Using the trigonometric function,
                                     sin 60° = opposite / hypotenuse = 4 / hypotenuse
The value of the hypotenuse is 4.62 inches. Then, the diameter is twice this value which is 9.24 inches.