A wheelchair ramp has an angle of inclination of 10 degrees and rises to a height of 3ft. Determine the length of the ramp in feet.
1.5t^ +1.5t +176.4
To determine the length of the ramp, we need to use trigonometry. In this case, we can use the tangent function.
The tangent of an angle is defined as the opposite side divided by the adjacent side. In this scenario, the height of the ramp is the opposite side, and the length of the ramp is the adjacent side.
First, let's convert the angle from degrees to radians. We know that there are π radians in 180 degrees, so we can convert the angle as follows:
10 degrees * (π/180 degrees) = 10π/180 radians
Next, we can use the tangent function:
tan(10π/180) = height / length of ramp
We know the height is 3ft, so we can substitute it into the equation:
tan(10π/180) = 3 / length of ramp
Now, we can rearrange the equation to solve for the length of the ramp:
length of ramp = 3 / tan(10π/180)
Using a calculator or software capable of calculating trigonometric functions, we can find the value of tan(10π/180) ≈ 0.17364817766693033.
Substituting this value back into the equation:
length of ramp = 3 / 0.17364817766693033
Calculating this expression, we find that the length of the ramp is approximately 17.32 feet.