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

3 radians

Step-by-step explanation

Answer 2

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`

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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