Question

50 pts and brainliest. Is the ratio of arc length to r always equal to pi? What is it equal to?

Answer 1

Answer:

It can sometimes be equal to π. However, it is equal to our central angle.

Step-by-step explanation:

First, recall that arc length is given by:

$s=r\theta$

Where s is the arc length, r is the radius, and θ is the central angle of the arc in radians.

So, the ratio of the arc length to the radius is:

$\displaystyle \frac{r\theta}{r}$

The radius r cancels. Hence, we are left with:

$=\theta$

So, the ratio of the arc length to the radius does not equal π (although it can sometimes if the central angle is π radians (or 180°)). Rather, the ratio is equivalent to the central angle.

So, for example, if we have a circle with radius 7 with a central angle of 3π/2 (this gives us an arc length of 21π/2), then the ratio of the arc length to the radius will be 3π/2 (our central angle).

Answer 2

Answer:

Sometimes it can be equal to π. It is equal to our central angle.

Step-by-step explanation:

Recalling arc length is given by:

Where s is the arc length, r is the radius, and θ is the central angle of the arc in radians.

So, the ratio of the arc length to the radius is:

rθ/θ

The radius r cancels. Hence, we are left with:

= θ