Marks: 5 A hill that has a 15 % grade is one that rises 15.0 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal?

sinA = 15%/100% = 0.15

A = 8.63o

To find the angle at which the hill is inclined above the horizontal, you can use trigonometry. The tangent function can be used to find the angle.

The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the vertical rise of the hill is the side opposite the angle, and the horizontal distance is the side adjacent to the angle.

Let's denote the angle as θ.

Using the information provided, the vertical rise of the hill is 15.0 meters and the horizontal distance is 100.0 meters.

To find the tangent of the angle, θ, we can use the formula:

tan(θ) = opposite / adjacent = vertical rise / horizontal distance

So, plugging in the values, we have:

tan(θ) = 15.0 / 100.0

Now, you can solve for θ by taking the inverse tangent (also known as arctan or atan) of both sides of the equation:

θ = arctan (15.0 / 100.0)

Using a scientific calculator or trigonometric table, you can find the value of arctan (15.0 / 100.0) as approximately 8.53 degrees.

Therefore, such a hill is inclined approximately 8.53 degrees above the horizontal.