Question

A wheelchair ramp has a slope of 1:12 (1 foot of rise over a horizontal distance of 12 feet). To the nearest 0.1 foot, how many feet of ramp will be needed to rise 3 feet? (Round the angle of incline to the nearest 0.01°.)

Answer 1

In the figure attached you can see two triangles: triangle A and triangle B.

1. We must find the value of the angle "α" of the triangle A:

Tan^-1(α)=Opposite Leg/Adjacent leg

Opposite leg=1
Adjacent leg=12

Tan^-1(α)=1/12
α=4.8°

2. Now, let's find the value of its hypotenuse "y":

Sin(α)=Opposite leg/Hypotenuse

Opposite leg=1
Hypotenuse=y

Sin(4.8°)=1/y
y=1/Sin(4.8°
y=12 ft

3. To rise 3 feet, the value of "x" (Feet of ramp), is:

1/12=3/x
x(1)=(3)(12)
x=36 ft

4. The angle of incline is:

Tan^-1(β)=Opposite Leg/Adjacent leg

Opposite leg=3
Adjacent leg=12

Tan^-1(β)=3/12
β=14°

How many feet of ramp will be needed to rise 3 feet?

The answer is: 36 feet