Sam built a ramp to a loading dock. The ramp has a vertical support 2 m from the base of the loading dock and 3m from the base of the ramp. If the vertical support is 1.2 m in height, what is the height of the loading dock?
Can someone please show me how to do this. I keep on getting 5 as an answer, and I know that that is not right
If I understand your description,
tan angle at bottom of ramp = 1.2/3.
Then tan angle = x/5.
Check my thinking.
yes
To find the height of the loading dock, we can use the concept of similar triangles.
Let's denote the height of the loading dock as "x".
According to the problem, we have a vertical support 2 m from the base of the loading dock, which means the height on the loading dock side is also 2 m.
We also know that the vertical support is 1.2 m in height.
Now, we can set up a proportion between the corresponding sides of the two similar triangles:
(x / 1.2) = ((x + 2) / 3)
To solve for x, we can cross-multiply and solve the resulting equation:
3x = 1.2(x + 2)
Expanding the equation:
3x = 1.2x + 2.4
Simplifying the equation:
3x - 1.2x = 2.4
2.8x = 2.4
Dividing both sides by 2.8:
x = 2.4 / 2.8
x ≈ 0.857
So, the height of the loading dock is approximately 0.857 meters.
To solve this problem, we can use similar triangles. Similar triangles have proportional sides.
Let's label the height of the loading dock as "h".
We have two similar triangles - one formed by the support, the ramp, and the height difference, and the other formed by the loading dock, the ramp, and the height difference.
Using the first triangle, we can set up the following proportion:
h / 1.2 = (h - 2) / 3
Cross-multiply to solve for h:
3h = 1.2(h - 2)
Simplify the equation:
3h = 1.2h - 2.4
Combine like terms:
3h - 1.2h = -2.4
Find the value of h:
1.8h = -2.4
Divide both sides of the equation by 1.8:
h = -2.4 / 1.8
Therefore, the height of the loading dock is approximately -1.33 meters.
It's important to note that when working with real-world problems, negative values for measurements do not make sense. In this case, it suggests that there might be an error in our calculations or initial assumptions.