Question

An arc with length 5 pi over 4 inches is formed by a 15 degree central angle what is the radius of the circle

Answer 1

Answer:

Radius of the circle is 15 inches.

Step-by-step explanation:

Relation between length of arc, radius and the angle subtended by the arc on center is:

$\theta = \dfrac{l}{r} ..... (1)$

where $\theta$ is the central angle in radians subtended by arc

$l$ is the length of arc

$r$ is the radius of arc

We are Given the following details:

$l = \dfrac{5\pi}{4}\ inch$

$\theta = 15^\circ$

We know that $\pi \ radians = 180 ^\circ$

Converting $\theta$ to radians:

$\theta =\dfrac{\pi}{180} \times 15$ radians

Putting the values of $\theta$ and $l$ to find the value of $r$

$\dfrac{\pi}{180} \times 15 = \dfrac{5\pi}{4r}\\\Rightarrow r = \dfrac{45}{3} \\\Rightarrow r = 15 \ inches$

Hence, Radius of the circle is 15 inches.