Question

according to the americans with disabilities act, a ramp can rise no more than 1 ft for every 12 ft of horizontal distance. what is the maximum angle that the ramp can form with the ground? a. 4.8° c. 5.0° b. 2.7° d. 3.7° please select the best answer from the choices provided

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle $\theta$ in a right - triangle is given by $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In the case of the ramp, the vertical rise is the opposite side and the horizontal distance is the adjacent side. Here, the vertical rise (opposite) is $1$ ft and the horizontal distance (adjacent) is $12$ ft, so $\tan\theta=\frac{1}{12}$.

Step2: Find the angle

We need to find $\theta$ such that $\tan\theta = \frac{1}{12}$. Using the inverse - tangent function, $\theta=\tan^{- 1}(\frac{1}{12})$.
Calculating $\tan^{-1}(\frac{1}{12})\approx4.8^{\circ}$ (using a calculator in degree mode).

Answer:

A. $4.8^{\circ}$