The bottom end of a 14 foot loading ramp is 10.7 feet away from the entrance to the building. Find the angle the ramp makes with the ground.
r = 14 Ft.
X = 10.7 Ft.
CosA = X/r
To find the angle the ramp makes with the ground, we can use trigonometry. Specifically, we can use the tangent function.
First, let's label the sides of the right triangle formed by the ramp, the ground, and the height of the building. The side opposite the angle we want to find is the height of the building (14 feet), and the side adjacent to the angle is the horizontal distance from the bottom end of the ramp to the entrance of the building (10.7 feet). The hypotenuse of the triangle is the ramp itself.
Now, we can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side:
tan(angle) = opposite / adjacent
In this case, we want to find the angle, so we rearrange the equation:
angle = arctan(opposite / adjacent)
Plugging in the values, we have:
angle = arctan(14 / 10.7)
To find this angle, you can use a scientific calculator or an online calculator that has an inverse tangent function (often denoted as "tan⁻¹" or "atan"). Simply input "14 / 10.7" into the calculator and take the inverse tangent of that value. The resulting angle is the angle the ramp makes with the ground.