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?

Question

asked Nov 26, 2021 5.3k views

2 Answers

Interactive · Answer 1 · 2021-12-02T10:19:15+0000

Answer:

is 171.8 degrees

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