The grade of a highway up a hill is 15%. How much change in horizontal distance is there if the vertical height of the hill is 650 feet? Express the answer to the nearest foot.
A)4,352 ft
B)4,333 ft
C)4,233 ft
D)4,343 ft
E)4,308 ft

Question

Quizplus · Accepted Answer

To find the horizontal distance, we need to use trigonometry. We know that the grade of the highway is 15%, which means that for every 100 feet of horizontal distance, there is a 15-foot increase in elevation. We can use this to set up a proportion:

15/100 = 650/x

Where x is the horizontal distance we want to find.

To solve for x, we can cross-multiply and simplify:

15x = 65000
x = 4333.33

Rounding to the nearest foot gives us:

x ≈ 4333 ft

Therefore, the best choice is B) 4,333 ft.

The Grade of a Highway Up a Hill Is 15