Question

Convert \[{115^{\circ}}\] to radian?

Answer 1

Hint: In this question we are asked to convert the given degree into radians, and this can be converted using the conversion formula i.e.,${x^{\circ}} = {x^{\circ}} \times \dfrac{\pi }{{{{180}^{\circ}}}}$ radians, and substituting the number of degrees i.e. $x$ in this formula we will get the required converted radians.

Complete step by step solution:
Degrees and radians are ways of measuring angles. A radian is equal to the amount an angle would have to be open to capture an arc of the circle's circumference of equal length to the circle's radius. ${360^0}$ (360 degrees) is equal to $2\pi $radians.
Given degree is \[{115^{\circ}}\],
We have to convert the degree into the radians, by using the conversion formula.
We know that ${180^0} = \pi $ radians, then we can write 1 degree as, ${1^{\circ}} = \dfrac{\pi }{{{{180}^{\circ}}}}$,
Now using the formula ${x^{\circ}} = {x^{\circ}} \times \dfrac{\pi }{{{{180}^{\circ}}}}$we can convert 37 degrees into radians, here$x = {115^{\circ}}$,
By substituting the value of $x$ in the formula, we get,
$ \Rightarrow {115^0} = {115^{\circ}} \times \dfrac{\pi }{{{{180}^0}}}$,
By simplifying we get,
$ \Rightarrow {37^0} = \dfrac{{23\pi }}{{36}}$radians.

Final Answer:
$\therefore $ The radians form when we convert 115 degrees to radians is equal to $\dfrac{{23\pi }}{{36}}$.

Note:
There is a chance that students can make mistake while solving these type of questions in taking formula for conversion of angle to radians as, ${1^0} = \dfrac{\pi }{{{{360}^0}}}$radians, as it is a wrong formula a ${360^0} = 2\pi $ then we can write it as, ${1^{\circ}} = \dfrac{{2\pi }}{{{{360}^{\circ}}}} = \dfrac{\pi }{{{{180}^{\circ}}}}$ radians.${360^0} = 2\pi $ .
Degrees are more common in general: there are 360 degrees in a whole circle, 180 degrees in a half circle, and 90 degrees in a quarter of a circle. A radian is the amount an angle has to open such that the length of the section of the circle's circumference it captures is equal to the length of the radius.