Question

How do you find the radian measure of a central angle of a circle of radius 14.5 centimeters that intercepts an arc of length 25 centimeters?

Answer 1

Hint: In this question, we have to find the radian measure of a central angle of a circle of radius 14.5 centimeters that intercepts an arc of length 25 centimeters. The angle can be obtained by the formula $\theta = \dfrac{s}{r}$. Substitute the values in the formula and do simplification to get the desired result.

Complete step by step answer:
The plane angle subtended by a circular arc is defined by Radian as the arc length divided by the radius of the arc. The angle subtended at the middle of a circle by an arc equal in length to the radius of the circle is a radian.
Radian is presumed where no symbol is used. The symbol $^\circ $ is written when degrees are the unit of an angular scale. Note that, in the international system of units, a radian is a derivative unit.
So, the radius of the circle is 14.5 centimeters.
The arc length of the circle is 25 centimeters.
Now, the formula the radian measure of any angle at the center of a circle is,
$\theta = \dfrac{s}{r}$
Where $\theta $ is the angle in radians
$s$ is the intercepted arc
$r$ is the radius of the circle
Substitute the values in the above formula,
$ \Rightarrow \theta = \dfrac{{25}}{{14.5}}$
Divide numerator by the denominator,
$ \Rightarrow \theta = 1.724$

Hence, the angle measure in radians is 1.724.

Note: Note that to translate from degrees to radians, the angle must be separated by 180. Multiply the angle by 180 to translate from radians to degrees. A single radian is roughly \[57.3^\circ \] in terms of degrees. An angle of $1^\circ $, likewise, is roughly 0.017 radians.