1. By pedaling, you turn the large gear through an angle of 60°. AD = 5 inches, and BC = 3 inches. CD, the length of the chain between the gears, is 17 inches. How far does the chain move around the circumference of the gear to the nearest tenth of an inch?

2. As the chain moves, it turns the small gear. If you use the distance you calculated in the previous question, through what angle does the small gear turn to the nearest degree?
A. 100° B. 120° C. 112° D. 106°

Question

1. By pedaling, you turn the large gear through an angle of 60°. AD = 5 inches, and BC = 3 inches. CD, the length of the chain between the gears, is 17 inches. How far does the chain move around the circumference of the gear to the nearest tenth of an inch? 

2. As the chain moves, it turns the small gear. If you use the distance you calculated in the previous question, through what angle does the small gear turn to the nearest degree?
A. 100°     B. 120°     C. 112°     D. 106°

anonymous · Answer

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anonymous · Answer

The first part is just an arc length question. $$s = r \theta$$, where r is the radius of the gear and theta is the change, in radians, of the central angle of the gear.The second part, you need to use the arc length in the first part and set it equal to a new equation to find the change in the central angle of the smaller gear.