Associated Topics || Dr. Math Home || Search Dr. Math

### 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

```
Associated Topics:
High School Trigonometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search