A hill that has a 17.5% grade is one that rises 17.5 m vertically for every 100.0 m of distance in the horizontal direction. At what angle is such a hill inclined above the horizontal?
tan^-1 0.175 = 9.93 degrees
fawelrihefjposeui
A gallon of water sample occupies a volume of 3.785 times 10-3. The mass of the water sample is 3.785 kg. What is the density of water in kg/m^3 ?
To find the angle at which the hill is inclined above the horizontal, you can use the trigonometric function called tangent. The tangent of an angle is defined as the ratio between the length of the opposite side and the length of the adjacent side of a right triangle.
In this case, the opposite side represents the vertical rise of the hill (17.5 m) and the adjacent side represents the horizontal distance (100.0 m). Therefore, the tangent of the angle θ (the angle at which the hill is inclined above the horizontal) is given by:
tan(θ) = opposite/adjacent = 17.5/100.0
To find the value of θ, you need to take the inverse tangent (also known as arctangent or tan^(-1)) of both sides of the equation:
θ = arctan(17.5/100.0)
Using a calculator, you can find the arctan of 17.5 divided by 100.0 to get the angle θ.
Therefore, the angle at which the hill is inclined above the horizontal is θ degrees.