Question 1205123
To find the angle of inclination of the hill, we can use trigonometric ratios. Let's denote the angle of inclination of the hill as θ.
The tangent of an angle is defined as 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 side opposite the angle θ is the height of the water tower (30 m), and the side adjacent to the angle θ is the distance down the hill (120 m).
tan(θ) = opposite/adjacent
tan(θ) = 30/120
tan(θ) = 1/4
Solve for θ by taking the inverse tangent (arctan) of both sides of the equation.
θ = arctan(1/4)
Using a calculator or a trigonometric table, we can find the value of θ to be approximately 14.04°.
Therefore, the angle of inclination of the hill is approximately 14.04°.