Question

3. Shana is about to perform a relay handoff on a circular track that has a

radius of 9 meters and her track partner Katie is standing 132° away from
her. How many meters does Shana need to run to pass the baton to Katie?

Answer 1

Shana needs to run approximately 20.79 meters to pass the baton to Katie, calculated by converting the central angle of 132° to radians and using the formula for arc length on a circle given the radius of 9 meters.

Step-by-step explanation:

To calculate the distance Shana needs to run to pass the baton to Katie on a circular track, we need to determine the length of the arc between them, which is a section of the track. The formula to calculate the arc length (s) is s = rθ, where r is the radius of the circle (track) and θ is the central angle in radians. First, convert the angle from degrees to radians because the standard measurement unit for angles in arc length calculations is radians.

To convert from degrees to radians, multiply the angle in degrees by (π/180). In this case:
θ (in radians) = 132° × (π/180°) = (132°/180°) × π = 2.31 radians (approx).

Now we have the radius r = 9 m and θ = 2.31 radians. Applying the formula:

s = rθ = 9 m × 2.31 radians = 20.79 m (approx).

Therefore, Shana needs to run approximately 20.79 meters to pass the baton to Katie.

Answer 2

Shana need to run 20.74 meters to pass the baton to Katie.

Step-by-step explanation:

The radius of the circular track for the relay handoff race is 9 meters.

Therefore, the total length of the circular track is the circumference of the circle i.e.
`2\pi r = (2 * 22 * 9)/(7) = 56.57` meters.

Shana is about to perform the race and her partner Katie is standing 132° away from her.

We have to calculate the circular track distance from Shana to Katie.

Now, 360° rotation is equivalent to a circular length of 56.57 meters.

Hence, 132° rotation will be equivalent to
`(56.57 * 132)/(360) = 20.74` meters.

Therefore, Shana needs to run 20.74 meters to pass the baton to Katie. (Answer)