Find the angle and length in a given scenario

Question

You are going to install a wheelchair ramp over a straight, horizontal path that runs from the sidewalk to your deck. Your deck is 1.5 feet higher than the path and you want the grade of the ramp to be 6.75%.

a.) What is the angle,θ, that the ramp forms with the path? Round 5 decimal places.

b.) How long does the path have to be to install this ramp? Round 3 decimal places.

c.) What length ramp should you install, that will reach from the ground to the deck? Round 3 decimal places.

Answer 1

1) θ = arctan(.0675)

2) x length in feet = 1.5 ft cot(θ) θ from (a) or simply 1.5/.0675

3) ramp length in feet = 1.5 ft / sin(θ)