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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.

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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.

The diameter of the plate. show all work. will be 9.24 inches. The diameter is double of the hypotenuse.

What is the diameter?

A diameter is a line that travels through the center of an object and intersects the circumference at opposing ends. It measures twice as long as the object's radius.

The radius of the circle becomes the hypotenuse when a right triangle is formed by joining the edge of the knife to the center of the circle and the center of the knife to the center of the circle.

With the help of the trigonometric function, the value of the hypotenuse is found as;

[tex]\rm sin \ 60^0 = \frac{8}{h} \\\\ h= 4.62 \ inch[/tex]

The diameter of the plate is double the hypotenuse in the given figure;

[tex]\rm D = 2 \times h \\\\ D = 2 \times 4.62 \\\\ D= 9.24 \ inch[/tex]

To learn more about the diameter refer to the link;

https://brainly.com/question/5501950

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