Question

Two bicycle ramps each cover a horizontal distance of 8 feet. Once ramp has a 20° angle of elevation, and the other ramp has a 35° angle of elevation

How much taller is the second ramp than the first?

Answer 1

So below I’ve attached an image for the ramps.
We are given two ramps, both covering 8ft horizontally. One ramp has 20 degrees of elevation, another has 35 degrees.
Let’s separate the two ramps using x and y.
And let’s solve:
Because it’s a right triangle, we will be using sine, cosine, or tangent to find the missing side (vertical).
We will use tangent because tangent is opposite/adjacent. We have the adjacent side, and we need to find the opposite side.
So let’s solve the first one:
tan20degrees=x/8
x=2.9ft

And now the second:
tan35degrees=y/8
y=5.6ft

Now subtract the second by the first to find the difference in height:
5.6-2.9=2.7

The second ramp is 2.75ft taller than the first.

Hope this helped!