Edward wants to compare slope of two wake board ramps. The first ramp has the rise of 5 feet and run of 12 feet. The second has the rise of 6 feet and the run of 3 feet. Find the slope of each ramp. Which ramp is steeper?

Step-by-step explanation:

The formula for determining the slope of a ramp is expressed as

Slope = rise/run

The first ramp has the rise of 5 feet and run of 12 feet. This means that the slope of the first ramp is

Slope = 5/12 = 0.417

The second has the rise of 6 feet and the run of 3 feet. This means that the slope of the second ramp is

Slope = 6/3 = 2

The lower the run, the steeper the slope. This means that the second ramp is steeper than the first ramp.

This can be confirmed by calculating the angle formed by each ramp. To determine the angle formed by the ramp with the horizontal, we would apply we would apply

the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side.

Considering the first ramp,

Tan θ = 5/12 = 0.417

θ = Tan^-1 (0.417)

θ = 22.6°

Considering the second ramp,

Tan θ = 6/3 = 2

θ = Tan^-1 (2)

θ = 63.4°

The second ramp forms a greater angle. Thus, it is steeper.