The grade of a road is 6%. What is its angle of elevation?
find x such that tan(x) = 0.06
To find the angle of elevation of a road given its grade, you can use basic trigonometry. The grade of a road is the ratio of its vertical rise to its horizontal run, expressed as a percentage.
Let's denote the grade of the road as "g." In this case, g = 6%. "g" represents the ratio of the vertical rise to the horizontal run, so it can be expressed as g = rise/run.
To find the angle of elevation, we can use the inverse tangent function (arctan) because tangent is the ratio of the opposite (rise) to the adjacent (run) side of a right triangle. The formula is:
angle of elevation = arctan(g)
Now, let's substitute the given grade into the formula:
angle of elevation = arctan(6%)
To solve this, use a scientific calculator with an arctan or inverse tangent function. Enter the grade (0.06) in decimal form and calculate the arctan. The result will be the angle of elevation of the road.
Note: Make sure your calculator is in degree mode, as the angle of elevation is usually expressed in degrees.