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

Answer:[tex]\displaystyle \frac{25}{2}\pi \approx 39.3[/tex] 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?[tex]\text{Circumference} = \pi \times \text{Diameter} = 2\pi \times \text{Radius} = 30\pi[/tex] inches.However, this wiper traveled only a fraction of the circle. A full circle is [tex]360^{\circ}[/tex]. The central angle of this arc is only [tex]150^{\circ}[/tex]. As a result,[tex]\displaystyle \frac{\text{Length of this arc}}{\text{Circumference of the circle}} = \frac{150^{\circ}}{360^{\circ}} = \frac{5}{12}[/tex].The length of the arc will thus be[tex]\displaystyle \frac{5}{12} \times 30\pi = \frac{25}{2}\pi \approx 39.3[/tex].In other words, the windshield wiper traveled approximately 39.3 inches.