A ramp 17.5 feet in length rises to a loading platform that is 3 1/3 feet off the ground. Find the angle that the ramp makes with the ground.
I'm so confused. I hate physics so much!
YOU SHOULD KNOW
To find the angle that the ramp makes with the ground, we can use trigonometry.
The ramp forms a right triangle with the ground and the height of the loading platform. The length of the ramp is the hypotenuse of this right triangle, and the height of the loading platform is the opposite side.
We can use the tangent function to find the angle. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the loading platform, and the adjacent side is the length of the ramp.
Let's calculate it step by step.
Step 1: Convert the length of the ramp to inches
Given that the length of the ramp is 17.5 feet, we need to convert it to inches since the height is given in feet. There are 12 inches in a foot, so we multiply the length by 12 to get:
17.5 feet * 12 inches/foot = 210 inches
Step 2: Calculate the angle using the tangent function
Now, we can use the tangent function to calculate the angle. The tangent of an angle θ is equal to the opposite side divided by the adjacent side. Rearranging the equation gives us:
θ = arctan(opposite/adjacent)
θ = arctan(height of loading platform/length of ramp)
θ = arctan(3 1/3 feet/210 inches)
To make the calculations easier, we need to convert the height of the loading platform to inches. Since there are 12 inches in a foot, we have:
3 1/3 feet * 12 inches/foot = 40 inches
Now, we can substitute the values into the equation:
θ = arctan(40 inches/210 inches)
Using a calculator or trigonometric table, we find:
θ ≈ 10.65 degrees
Therefore, the angle that the ramp makes with the ground is approximately 10.65 degrees.