Question

the steepness, or grade, of a highway or railroad is expressed as a percent. in the photo of the cog railway at pikes peak, in colorado, the grade is 18%. thus, for every 100 ft of horizontal run, the train rises 18 ft. find the angle of the inclination of the railway. a. 10.2° b. 15.7° c. 7.85° d. 19.2° please select the best answer from the choices provided

Explanation:

Step1: Recall the tangent - ratio formula

The grade of a slope is the ratio of the vertical rise to the horizontal run. If the horizontal run is $x = 100$ ft and the vertical rise is $y=18$ ft, and the angle of inclination is $\theta$, then $\tan\theta=\frac{y}{x}$.

Step2: Calculate the tangent value

Given $x = 100$ and $y = 18$, we have $\tan\theta=\frac{18}{100}=0.18$.

Step3: Find the angle using the inverse - tangent function

We know that $\theta=\arctan(0.18)$. Using a calculator in degree mode, $\theta=\arctan(0.18)\approx10.2^{\circ}$.

Answer:

A. $10.2^{\circ}$