solve problem

Question

In a circle of radius 120 cm, an arc 344 cm long subtends an angle of how many radians? How many degrees?

The arc subtends an angle of _____radians               How many degrees_____________

 

      

Answer 1

I followed a different path than Muhammad C to find the same answer.

 

First I want to know what the total circumference of the circle is.... C = (2)(pi)(r)

C = 2(3.14150(120) = 753.96 cm

 

Okay...  What part of that circumference does this arc take up?

 

We have 344 out of 753.96  or  344/753.96 = .45626 

 

So how much of the total 360 degrees is .45626...  or take .45626 of 360

.45626(360) = 164.25 degrees

 

Note however:  This only found the degrees, not the radians.  Thus, Muhammad C's answer is more complete.

Answer 2

You must use the equation s = r*theta where s represents arc length, r represents radius length & theta represents angle measure.

 

theta = s/r = 344cm/120cm = 43/15 radians = 2.866666 radians

 

The angle measure is 2.8666666 radians. To find the degree measure of this angle, we multiply the radians by 180/pi

 

(43/15)(180/pi) = 516/pi degrees = 164.25 degrees