A road has a grade of 28.4%. This means that the road rises 28.4 ft over a horizontal distance of 100 ft. What angle does the hill make with a horizontal line?
if the angle is x , then
tan(x) = .284
x = arctan(.284)
To find the angle that the hill makes with a horizontal line, we can use trigonometry.
Let's call the angle x. We know that the road rises 28.4 ft over a horizontal distance of 100 ft, which forms a right triangle.
The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the side opposite the angle x is the rise of the hill, which is 28.4 ft, and the side adjacent to the angle x is the horizontal distance, which is 100 ft.
So, the tangent of angle x can be calculated as:
tan(x) = (rise/ run) = 28.4/100
To find the angle x, we can take the inverse tangent (arctan) of both sides:
x = arctan(28.4/100)
Using a calculator or trigonometric table, we can find that arctan(28.4/100) is approximately 16.44 degrees.
Therefore, the angle that the hill makes with a horizontal line is approximately 16.44 degrees.