pre calc what formula would I use?

Question

This is the first year Valerie is playing softball and she has been practicing her batting. On her last swing the bat made an arc with a radius of 37.8 inches and swept through 214 degrees of rotation. Assuming the arc is circular, what is the distance the tip of the bat travels to the nearest hundredth of an inch?

Answer 1

s = r * theta in radians

Convert degrees to radians by multiplying by pi/180.

s = 37.4 * 214*pi/180 = about 141.18 inches.

Another way to find it is use Central Angle / 360 = Arc Length/Circumference

Circumference = 2 * pi * r

214/360 = x/(2*pi*37.8)

(2*pi*37.8)*214/360 = x = about 141.18 inches

Answer 2

Hello Samantha,

Because you're told to assume the arc is circular, you would use the arc length formula:

s = r *θ, where s = arc length; r = radius; θ is the central angle (or angle of rotation) in RADIANS.

They're asking you to find s: convert 214 degrees to radians, multiply that by the radius, and you will get the answer to the question.