A hill that has a 31.4 % grade is one that rises 31.4 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal?

(1) draw a right triangle.

(2) base = 100.0 m
(3) height = 31.4 m
(4) determine the angle (theta) between the base and the hypothenuse of the triangle.

Use tan theta = opposite side/adjacent side. don't forget to inverse tan.

How do you find the net force and its direction of the diagrams

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To determine the angle at which the hill is inclined above the horizontal, we can use the trigonometric relationship between the angle, the vertical height, and the horizontal distance.

First, let's assume that the horizontal distance is 100 units, as given in the question. In this case, the vertical height would be 31.4% of 100, which is 31.4 units.

Now, we can calculate the angle using the tangent function. The tangent of an angle is equal to the ratio of the opposite side (vertical height) to the adjacent side (horizontal distance). Mathematically, we can express this as:

tan(θ) = vertical height / horizontal distance

Plugging in the values, we get:

tan(θ) = 31.4 / 100

To find the angle (θ), we can take the inverse tangent (arctan) of both sides:

θ = arctan(31.4 / 100)

Using a calculator or math software, we find that the angle is approximately 17.98 degrees.

Therefore, a hill with a 31.4% grade is inclined approximately 17.98 degrees above the horizontal.