Question

9) An 8.2 km section of highway increases 870 m in elevation. The horizontal distance of the road is 8154m.

a) Calculate the slope to three decimal places
b) Calculate the angle of elevation to one decimal place. Tan x= opposite/adjacent
c) Calculate the percent grade to one decimal place. Percent Grade slope X 100

Answer 1

a) To calculate the slope, we divide the change in elevation by the horizontal distance:

870 m / 8154 m = 0.1065

So, the slope is 0.107 to three decimal places.

b) To calculate the angle of elevation, we use the tangent formula:

Tan x = opposite / adjacent = 870 m / 8154 m = 0.1065

So, x = tan^-1(0.1065) = 6.08°

The angle of elevation to one decimal place is 6.1°.

c) To calculate the percent grade, we multiply the slope by 100:

Percent grade = slope x 100 = 0.1065 x 100 = 10.7%

So, the percent grade to one decimal place is 10.7%.