Finding the Length of an Arc
Date: 2/14/96 at 11:52:42 From: Anonymous Subject: trig homework question I'm stuck on a homework problem - can you help me? (a) Find the length of arc that subtends an angle of measure 70 degrees on a circle of diameter 15 cm. (b) Find the area of the sector in part (a).
Date: 2/14/96 at 13:2:26 From: Doctor Ethan Subject: Re: trig homework question Here's a hint to get you going on these problems: Both the subtended arc length and the sector area are simply a fraction of the circle circumference/area, respectively, proportional to the ratio of the angle subtended by the whole circle. Well, that was quite a mouthful, so here's a simple example: Consider a circle with circumference C and area A. Let's examine a 90-degree sector of the circle. Since the angle subtended is 1/4 the total angle subtended by the circle (360), the arc length and area in the sector are C/4 and A/4 respectively. Basically, you're just taking fractional slices of the whole pie for which you have nice formulas for circumference and area. [Circumference = Pi*Diameter and Area = Pi*(Radius)^2] I hope this gives you a starting point from which to do your problems. -Doctor Ethan, The Math Forum
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