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