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:
[tex]\theta = \dfrac{l}{r} ..... (1)[/tex]
where [tex]\theta[/tex] is the central angle in radians subtended by arc
[tex]l[/tex] is the length of arc
[tex]r[/tex] is the radius of arc
We are Given the following details:
[tex]l = \dfrac{5\pi}{4}\ inch[/tex]
[tex]\theta = 15^\circ[/tex]
We know that [tex]\pi \ radians = 180 ^\circ[/tex]
Converting [tex]\theta[/tex] to radians:
[tex]\theta =\dfrac{\pi}{180} \times 15[/tex] radians
Putting the values of [tex]\theta[/tex] and [tex]l[/tex] to find the value of [tex]r[/tex]
[tex]\dfrac{\pi}{180} \times 15 = \dfrac{5\pi}{4r}\\\Rightarrow r = \dfrac{45}{3} \\\Rightarrow r = 15 \ inches[/tex]
Hence, Radius of the circle is 15 inches.
