Question

A circle has a radius of length r. If you mark off the an arc on the circle of length 3r, what is the measurement of the angle that subtends the arc?

Answer 1

Answer:

is 171.8 degrees

Step-by-step explanation:

Length of arc subtended by any angle $\alpha$ with a radius r is given by $\alpha *r$.

For example

to calculate length of circumference  

angle subtended by whole circle is 2$\pi$

Therefore length of circumference is $2\pi *r$

Similarly we can see that for semicircle angle at center is  $\pi$

hence length of arc is $\pi r$

____________________________________________

Given in the problem length of arc = 3r

radius= r

let the value of angle be $\alpha$

Plug in the value of length of arc in formula to calculate length of arc we have

3r = $\alpha* r$

$\alpha$ = 3r/r = 3

This value of angle subtended is in radian, we need to convert radian into degrees.

_____________________________________

We know that $\pi$ is equivalent to 180 degrees.

Also value of $\pi$ is 3.14

hence 3.14 radian= 180 degrees

=>3.14/3.14 = 180/3.14 ----degrees dividing both side with 3.14

=> 1 radian = 57.325 degrees

=> 1*3 radian = 57.325 * 3 degrees( multiplying both side with 3 as we need to find value of 3 radian into degrees

=> 3 radian = 171.8 degrees.

the measurement of the angle that subtended by  the arc is 171.8 degrees or in radian 3 radian