I need help with this question.

Question

Suppose you drive 0.9 miles on a road, during which the vertical distance changes from 0 to 220 feet. What is the angle of elevation (in degrees) of the road? Round to the nearest hundredth.

Answer 1

The units of miles in the "x-direction" and feet in the "y-direction" don't match so we need to convert them to the same unit of measure. How about converting 0.9 miles to feet?

Since there are 5280 feet in 1 mile, we can multiply 0.9 and 5280 to get the number of feet in 0.9 miles which turns out to be 4752 feet. Then draw a picture:

The trig function "tangent" is opposite/adjacent so that's what we want to use here. so we can say:

tan(θ) = 220/4752 and then to find θ, we use the inverse tangent so θ = tan^-1(220/4752) = 2.65°