Question

A street in San Francisco had a grade of 20%-

that is it rises 20 ft for every 100 ft
horizontally. What's the angle of elevation of the
street?

Answer 1

The angle of elevation for a street with a 20% grade is found using the arctangent of 0.20, which approximates to 11.31 degrees.

Step-by-step explanation:

To find the angle of elevation of the street with a grade of 20%, you can use the tangent function from trigonometry. The tangent of an angle in a right triangle is the ratio of the opposite side (rise) to the adjacent side (run). In this case, the rise is 20 feet, and the run is 100 feet.

You can use the formula tan(θ) = opposite/adjacent, which gives us tan(θ) = 20/100 or tan(θ) = 0.20. To find the angle θ, take the arctangent (also known as the inverse tangent) of 0.20.

Therefore, θ = arctan(0.20). Use a calculator to find that this is approximately 11.31 degrees.