Question

A 15 in. windshield wiper makes a 150° arc across the windshield.
About how far does the end of the windshield wiper travel?

Answer 1

Answer:

$\displaystyle \frac{25}{2}\pi \approx 39.3$ inches.

Step-by-step explanation:

The question gives the central angle and radius of an arc and is asking for the length.

• The radius is the same as the length of the windshield wiper: 15 inches.
• The central angle is 150°.

An arc is part of a circle. What is the circumference of a circle with a radius 15 inches?

$\text{Circumference} = \pi \times \text{Diameter} = 2\pi \times \text{Radius} = 30\pi$ inches.

However, this wiper traveled only a fraction of the circle. A full circle is $360^{\circ}$. The central angle of this arc is only $150^{\circ}$. As a result,

$\displaystyle \frac{\text{Length of this arc}}{\text{Circumference of the circle}} = \frac{150^{\circ}}{360^{\circ}} = \frac{5}{12}$.

The length of the arc will thus be

$\displaystyle \frac{5}{12} \times 30\pi = \frac{25}{2}\pi \approx 39.3$.

In other words, the windshield wiper traveled approximately 39.3 inches.