Question

Find the number of degrees subtended at the centre of the circle by an arc whose length is 0.357 times the radius.

Answer 1

Hint: We will use the formula $l=r\theta$ , where l is the arc length. And then we will substitute the value of l and r to find the value of $\theta$ , which is in radian. Then we will use the formula $\text{Angle in radian}=\dfrac{\pi }{180}\times \text{Angle in degree}$, to find the value of angle in degree.

Complete step-by-step answer:
Let’s solve this question by first using the formula $l=r\theta$ to find the angle in radian.
$l=0.357r$
Now substituting the value in $l=r\theta$ we get,
$\begin{aligned} & 0.357r=r\theta \\\ & \theta =0.357 \\\ \end{aligned}$
Now we will use the formula that helps us to convert radians into degrees.
The formula that converts radian into degree is:
$\text{Angle in radian}=\dfrac{\pi }{180}\times \text{Angle in degree}$
Now substituting the value of radian as o.357 in the above formula we get,
$\begin{aligned} & \text{Angle in degree}=\dfrac{180}{\pi }\times 0.357 \\\ & \text{Angle in degree}=\dfrac{180\times 7}{22}\times 0.357=20.44 \\\ \end{aligned}$
Hence, the answer to this question is $20.44{}^\circ$ .

Note: The formula that we have used for conversion is$\text{Angle in radian}=\dfrac{\pi }{180}\times \text{Angle in degree}$ and the arc length formula $l=r\theta$ must be kept in mind. From this formula we can also find the value of angle in degree if the value of angle in radian is given. So, in some questions the value of angle in radian might be given and we need to find the value of angle in degree, then also we will use the same formula for the purpose. We can also use the fact that 1 radian = 57.29 degree, and then we can multiply it by 0.357 to get the value of 0.357 radian in degree.