Question

What is the radian measure of \[72\] degrees?

Answer 1

Hint:
To measure angles, degrees and radians are used. This conversion of any angle in degrees to radians is used for the measurement in geometry. We can determine any angle in two forms that are degrees and radians. Converting one form to the other is therefore very important. To convert degrees to radians we need to use the below-given formula.
Formula:
Angle in radians \[ = \]angle in degrees\[ \times \dfrac{\pi }{{180}}\]

Complete answer:
We know that one radian is equal to \[\pi \]radians. To convert any degrees to radians we need to multiply the given angle in degrees and the value of \[\dfrac{\pi }{{180}}\].
Given that, we need to find the radians measure of\[72\]degrees.
Therefore substituting in the given formula,
Angle in radians \[ = \]\[72\]\[ \times \dfrac{\pi }{{180}}\]
\[{72^o} = \dfrac{{2\pi }}{5}rad\]

Therefore the radians measure of \[{72^o}\] is \[\dfrac{{2\pi }}{5}\] radians.

Additional Information:
Generally, in geometry, any angle is measured in angles. We use the other form of measuring the angle that is radians in trigonometry. The radians are usually represented in the form of \[\pi \]. The value of \[\pi \]is \[3.14\] or \[\dfrac{{22}}{7}\].

Note:
A measure of an angle that is when we draw a central angle of a circle that intercepts an arc then the length of the arc is equal to the radius of the circle is known as the radians. The SI unit for measuring angles is said to be radians. One radian is equal to approximately \[57.3\]. We have already seen the formula to convert degrees into radians. Now we can see the formula to convert radians into degrees. The formula for converting radians into degrees is that we need to multiply the given angle in degrees by \[\dfrac{{180}}{\pi }\].