Question

Jake and Rafael are training for a bike race. Jake is a beginner and starts by riding up a hill with a 7.9° incline. Rafael is more experienced and rides up a hill with an 18.3° incline. If Jake and Rafael ride 100 ft., how much more horizontal distance did Jake cover. A.4.1 ft. B.9.6 ft. C.17.7 ft. D. 19.2 ft.

Answer 1

We can use trigonometry to solve this problem. The horizontal distance covered by each rider can be found by multiplying the distance they rode by the cosine of the angle of incline. The difference between the two distances will be the amount by which Jake covered less distance than Rafael.

For Jake:

Horizontal distance = distance * cos(angle of incline)

Horizontal distance = 100 ft * cos(7.9°)

Horizontal distance = 100 ft * 0.9925

Horizontal distance = 99.25 ft

For Rafael:

Horizontal distance = distance * cos(angle of incline)

Horizontal distance = 100 ft * cos(18.3°)

Horizontal distance = 100 ft * 0.9475

Horizontal distance = 94.75 ft

Difference in horizontal distance = 99.25 ft - 94.75 ft

Difference in horizontal distance = 4.5 ft

Therefore, Jake covered 4.5 ft more horizontal distance than Rafael. The closest option is A. 4.1 ft, but that is not the exact answer.

Explanation:

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