Final answer:
To calculate the angle of elevation of a road, use the tangent function (tangent of the angle = rise/run) and then find the inverse tangent of the value obtained.
Step-by-step explanation:
To find the angle of elevation of the road, we can use trigonometry, specifically the tangent function, which relates the opposite side of a right triangle (the rise) to the adjacent side (the run or the length of the road). Here the rise is 400 meters and the run is 1.6 kilometers, which is 1600 meters. We apply the tangent function as follows:
tangent of the angle θ = opposite/adjacent = rise/run
tangent of the angle θ = 400 m / 1600 m = 0.25
Now we use the inverse of the tangent function to find the angle:
θ = arctan(0.25)
The calculator gives us the angle of elevation, which is the answer to the problem.