To the nearest degree, what angle does a hill with a grade of 11% make with a horizontal line?
A. 6*
B. 11*
C. 79*
D.84*
tan A = .11 = rise/run
A = 6 degrees 17 minutes
To find the angle that a hill with a grade of 11% makes with a horizontal line, you can use basic trigonometry.
The grade of the hill is given as a percentage, which represents the ratio of the vertical rise to the horizontal run. In this case, a grade of 11% means that for every 100 units of horizontal distance (the run), the hill rises by 11 units (the rise).
Now, let's set up a right triangle to visualize the situation. The vertical rise will be the side opposite to the angle we are trying to find, and the horizontal run will be the side adjacent to that angle. The hypotenuse of the triangle will represent the slope of the hill.
Using the trigonometric function tangent (tan), the equation to find the angle (θ) in degrees is tan(θ) = opposite/adjacent. In this case, the opposite side is 11 and the adjacent side is 100.
So, tan(θ) = 11/100
To solve for θ, take the inverse tangent (arctan) of both sides of the equation:
θ = arctan(11/100)
Using a calculator, the approximate value of θ is 5.7106 degrees.
Rounding this to the nearest degree, the angle that the hill makes with a horizontal line is 6 degrees.
Therefore, the correct answer is A. 6 degrees.