Question

A state park is designed in a circular pattern as shown. A park ranger drives along the circular path from the ranger station to the nature center and then from the nature center to the petting zoo. How far does he drive to the nearest tenth of a mile? A) 1.7 miles B) 2.3 miles C) 3.7 miles D) 4.7 miles

Answer 1

I saw the image.

Given:
Ranger Station to Nature Center = 90°
Nature Center to petting zoo = 40°
Petting Zoo to Tennis Court = 120°
Tennis Court to Pool = 65°
Pool to Ranger Station = 45°
radius = 1 mile

arc length = 2πr angle/360°

Ranger station to nature center.

arc length = 2 * 3.14 * 1 mile * 90°/360°
arc length = 2 * 3.14 * 1 mile * 0.25
arc length = 1.57 miles

Nature center to Petting Zoo

arc length = 2 * 3.14 * 1 mile * 40°/360°
arc length = 2 * 3.14 * 1 mile * 0.11
arc length = 0.70 miles

1.57 miles + 0.70 miles = 2.27 miles or 2.3 miles CHOICE B.