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
