Question

Grove Street has a grade of 20%. That means that the street rises 20 ft for every 100 ft of horizontal distance. To the nearest tenth, at what angle does Grove Street rise?

a) 11.3°
b) 16.7°
c) 18.4°
d) 20.0°

Answer 1

Using the arctangent function, the angle at which Grove Street rises, based on a grade of 20%, is approximately 11.3° to the nearest tenth.

Step-by-step explanation:

To determine the angle at which Grove Street rises based on a grade of 20%, we can use the concept of slope in relation to the angle of elevation. In this context, the slope given by the grade is the tangent of the angle of elevation. The slope is calculated as the rise over the run, which here is 20 ft over 100 ft.

We can use the arctangent function (inverse tangent) to calculate the angle, θ, from the slope:

tan(θ) = rise/run = 20/100 = 0.20

Using a calculator, we find that:

θ = arctan(0.20) ≈ 11.3°

Therefore, to the nearest tenth, Grove Street rises at an angle of approximately 11.3°.