Quandaries and Queries


Name: Melissa

Who is asking: Student

I am having some difficulties solving this problem. If you can give me any help, e-mail me and let me know. Thanks! A strip of wood is 16 ft. long and is bent in the arc of a circle. Two radii, from the center of the circle to the ends of the arc, form a right angle. What is the approximate distance from one end of the wooden arc to the other?



Hi Melissa,

In the diagram below P and Q are the ends of the wood strip, C is the center of the circle and r is its radius.

Ther circumference, D, of a circle is given by

D = 2 pi r. In your situation the wood strip is one-quarter the circumference so, using the expression above for the circumference you can find the radius r of the circle. Then the triangle PCQ is a right triangle, you know r so you can use Pythagoras' theorem to find the length of the hypotenuse.


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