According to the Americans With Disabilities Act, a ramp can rise no more than 1 ft for every 12 ft of horizontal distance. To the nearest tenth degree what is the maximum angle that the ramp can form with the ground?
tanTheta=1/12
theta= arctan (1/12)
To find the maximum angle that the ramp can form with the ground, we need to use the concept of trigonometry.
The ratio between the height of the ramp (rise) and the horizontal distance (run) can be represented by the tangent function (tan) of the angle formed by the ramp with the ground.
In this case, the rise of the ramp is 1 ft and the run is 12 ft. So, we can calculate the angle (θ) using the inverse tangent function (arctan) as follows:
θ = arctan(rise/run)
Substituting the values, we have:
θ = arctan(1/12)
Now, to find the value of θ to the nearest tenth degree, we need to use a scientific calculator or an online calculator that has the arctan function.
Using the arctan function, we find that θ ≈ 4.8 degrees.
Therefore, the maximum angle that the ramp can form with the ground, to the nearest tenth degree, is approximately 4.8 degrees.