Acar wheel has a 13-inch radius. through what angle does the wheel turn when the car rolls forward 3 ft?

158.7°

Step-by-step explanation:

Data:

r = 13 in

s = 3 ft

Calculations:

(a) Convert feet to inches

s = 3 ft × (12 in/1 ft) = 36 in

(b) Calculate the angle

Let θ = the angle subtended by the arc.

s = rθ

θ = s/r  = 36/13  ≈ 2.7692 rad

Convert radians to degrees

2.7692 rad × (360°/2π rad) = 158.7°

The wheel travels through an arc of 158.7°.

Step-by-step explanation:

Givens:

refers to the length of the circumference, which is the same distance rolled.

So, to find the angle, we have to use this definition:

; which is the relation between arc, angle and length.

Before, replacing all values, we have to transform 13 inches in feet. We know that 1 feet is 12 inches. So,

Now, we find the angle.

Therefore, the angle is 2.78 radians.

To have it in degrees, we have to transform.