Question

The length of the 135˚ arc below is 15/4 π. Find the radius of the circle. Please explain the answer.

Answer 1

Answer:

The radius of the arc is 5

Step-by-step explanation:

An arc is a part of the circumference of a circle that has been cut out. It can be best understood as an incomplete circle. The length of the arc is how long the arc is.

The formula relating how long the arc is with its radius is

length of arc = $\frac{\theta}{360} \times 2 \pi R$

where R is the radius we are looking for.

Θ = 135 which can be seen as the arc angle

$R =\frac{l \times 360}{\theta \times 2 \pi} =\frac{(15 \pi /4) \times 360 }{135 \times 2 \pi}=5$

The radius of the arc = 5