Question

What is the arc length if θ = 7 pi over 4 and the radius is 5?

Answer 1

Answer: The required arc length will be 27.5 units.

Step-by-step explanation: We are given to find the arc length with the following information :

`\theta=(7\pi)/(4),~~~\textup{radius},~r=5.`

We know that the length of an arc with angle subtended at the center α and radius of the circle r units is given by

`\ell=r\alpha.`

Therefore, the required arc length will be

`\ell=r\theta=5*(7\pi)/(4)=(35)/(4)* (22)/(7)=(5* 11)/(2)=(55)/(2)=27.5.`

Thus, the required arc length will be 27.5 units.

Answer 2

The formula for arc length is:

s= r∅

Given that ∅= 7π/4

and r= 5

Therefore, arc length s= 7π/4 *5 = 35π/4