The maximum slope of a wheelchair ramp is 1:12. For a wheelchair ramp made with these specifications, what angle does the ramp make with the ground? Round your answer to the nearest hundredth.
Since the angle is what needs to be found, the formula should be an inverse one. So the equation should be tan^-1(1/12). Which will give the answer 4.76.
tan(Θ) = 1 / 12
To find the angle that the ramp makes with the ground, we can use trigonometry.
The slope ratio of 1:12 can be expressed as a fraction, where the vertical rise is 1 unit and the horizontal run is 12 units.
Let's denote the angle as θ.
The tangent of θ is equal to the ratio of the rise to the run:
tan(θ) = 1/12
To find θ, we can take the arctangent (inverse tangent) of both sides:
θ = arctan(1/12)
Using a calculator, we can evaluate this:
θ ≈ 4.76 degrees
Therefore, the ramp makes an angle of approximately 4.76 degrees with the ground.
To find the angle that the wheelchair ramp makes with the ground, we can use the concept of trigonometry.
The slope of a ramp is defined as the ratio of the vertical rise to the horizontal run. In this case, the maximum slope is 1:12. This means that for every 12 units of horizontal distance, the ramp rises 1 unit vertically.
The angle of the ramp, denoted as θ, can be found using the tangent function. The tangent of an angle is equal to the ratio of the opposite side (vertical rise) to the adjacent side (horizontal run).
In this case, the opposite side of the triangle represents the vertical rise (which is 1 in our case) and the adjacent side represents the horizontal run (which is 12 in our case).
Therefore, we can use the formula: tan(θ) = opposite/adjacent.
tan(θ) = 1/12
To find the angle θ, we can take the inverse tangent (also known as arctan or atan) of both sides of the equation.
θ = atan(1/12)
Using a calculator, we can find the value of arctan(1/12) to be approximately 4.76 degrees.
Therefore, the angle that the wheelchair ramp makes with the ground is approximately 4.76 degrees.