Question

How do you convert $2.5$ radians to degrees?

Answer 1

Hint: Here, we will use the conversion formula of converting radians to degrees. We will multiply the converting factor to the given measurements and then by using the unitary method we will find the required answer. The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.

Formula Used:
1 radian $ = {\left( {\dfrac{{180}}{\pi }} \right)^\circ }$.

Complete step-by-step answer:
As we know, in degrees, one complete counterclockwise revolution is of $360^\circ $ but in radians, it is $2\pi $
Hence, we can write this as:
$2\pi $ radians $ = 360^\circ $
Or
$\pi $ radians $ = 180^\circ $
By unitary method, we can also write this as,
1 radian $ = {\left( {\dfrac{{180}}{\pi }} \right)^\circ }$
Hence, we get the conversion formula of converting radian measure to degree measure as:
$\dfrac{{180^\circ }}{\pi }$ radians
In order to convert $2.5$ radians to degrees we will use the conversion formula of radians to degree measure.
Multiplying ${\left( {\dfrac{{180}}{\pi }} \right)^\circ }$ by $2.5$, we get
$2.5$ radians $ = {\left( {\dfrac{{180}}{\pi }} \right)^\circ } \times 2.5$
Substituting the value of $\pi = 3.14$, we get,
$ \Rightarrow 2.5$ radians $ = \dfrac{{180}}{{3.14}} \times 2.5$
Converting decimal into fraction, we get
$ \Rightarrow 2.5$ radians $ = \dfrac{{180}}{{314}} \times \dfrac{{25}}{{10}} \times 100$
Multiplying the terms, we get
$ \Rightarrow 2.5$ radians $ = \dfrac{{22500}}{{157}} = 143.3^\circ $

Therefore, $2.5$ radians is equal to $143.3$ degrees.

Thus, this is the required answer.

Note: In mathematics, degrees are a unit of angle measure. A full circle is divided into 360 degrees and hence, a quarter of a circle, which forms a right angle is equal to one-fourth of 360 degrees i.e. 90 degrees. A degree has a symbol $^\circ $ and hence, right angle $ = 90^\circ $. Now, another unit to measure angles is called radian. 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.