Question

What is \[\dfrac{{5\pi }}{6}\] radians in degrees?

Answer 1

Hint: Here, this question belongs to the conversion topic that is we have to convert the unit from one form to another. Here we have to convert the unit radians to the unit degree as we know that the Radians and degrees is unit of angle. To solve this, we have to multiply \[\dfrac{{180}}{\pi }\] to the given radian of angle and simplify to get the required solution.

Complete step by step solution:
Conversion of Units is a multi-step process that converts units of measurement for the same quantity. It includes division or multiplication by a numerical factor or rounding off the significant digits.
 Radian and Degrees are both units of measurements of the angle.
The radian is a unit of angular measure defined such that an angle of one radian subtended from the centre of a unit circle produces an arc with arc length 1. A full angle is therefore \[2\pi \]radians, so there are \[{360^0}\] per \[2\pi \]radians, equal to \[\dfrac{{{{180}^0}}}{\pi }\] or \[\;{57.29577951^0}\]. i.e., \[\;{\pi ^c}\] radians are equal to \[{180^0}\] degrees.
To convert from degree to radian we multiply the angle by: \[\dfrac{\pi }{{180}}\].
To convert from radian to degree we multiply the angle by: \[\dfrac{{180}}{\pi }\].
Now, consider the given question, we have to convert \[\dfrac{{5\pi }}{6}\] radians to degrees.
To convert this, multiply by \[\dfrac{{180}}{\pi }\] to the given radians of angle i.e.,
 \[ \Rightarrow \dfrac{{5\pi }}{6} \times \dfrac{{180}}{\pi }\]
 \[ \Rightarrow 5 \times 30\]
 \[ \Rightarrow 150\] degrees.
Hence, \[\dfrac{{5\pi }}{6}\] radian = \[150\] degree.
So, the correct answer is “ \[150\] degree”.

Note: We have different units for solid quantity, liquid quantity and gaseous quantity. Every quantity has a measurement unit from the low quantity to the high quantity. While converting the unit of a quantity from one form to another form we have standard value. By multiplying or dividing we can convert the unit of the quantity. We have a different system of measurement of a quantity.