Awheelchair 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°.)

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