The tip of a 15-inch wiper blade wipes a path that is 36 inches long. What is the angle of rotation of the blade in radians to the nearest tenth?

2.4 radians

1.2 radians

2.8 radians

0.4 radians

The length of the arc is a fraction of the circumference of the circle depending on the length of the radius and the intercepted angle. This can be calculated through the equation,

L = (2πr) x (θ / 360)

where L is the length of arc, r is the radius, and θ is the intercepted angle in terms of degrees.

Substituting the known values to the equation,

36 = (2π) (15) x (θ / 360)

We translate the equation to find the value of θ,

θ = (36) (360) / 2π (15)

The value of θ is equal to 137.51°.

This can be coverted to radians through the equation below,

θ (in radians) = 137.51° x (2π rad / 360°) = 2.4 rad