To understand what a grade of 7 means, we need to interpret it as a slope. A grade of 7 indicates that for every 100 feet of horizontal distance, the road rises 7 feet vertically.
We can find the angle that the road makes with the horizontal by using the tangent function, which is defined as the opposite side (vertical rise) divided by the adjacent side (horizontal distance). In this case:
tan(θ) = (vertical rise) / (horizontal distance) = 7 / 100
To find the angle θ, we can take the arctangent (inverse tangent) of the slope:
θ = arctan(7 / 100)
Now we need to calculate this value using a scientific calculator or a programming tool that can compute the arctangent in radians. When calculated, this gives us:
θ ≈ 0.0698 radians
This means that the angle the road makes with the horizontal is approximately 0.0698 radians.