This is a repost from a few weeks ago from someone esle but need help.
The ramp shown below is used to move crates of oranges to loading docks at different heights. When the horizontal distance AB is 15ft, the height of the loading dock, BC, is 3ft. What is the height of the loading dock DE?
-5
-8
-9
-25
My answer: 5
Diagram: a Right triangle, a line through the triangle so it is ABC and then the other side is BCDE. (ABC looks like a right triangle and BCDE looks likea trapazoid kinda. Sorry if this doesnt make sense.)
To find the height of the loading dock DE, we can use the concept of similar triangles.
First, let's label the points in the diagram:
A: The starting point of the ramp
B: The top of the ramp
C: The bottom of the ramp
D: The top of the loading dock
E: The bottom of the loading dock
Since triangle ABC is a right triangle, we can use the Pythagorean theorem to find the length of BC:
BC^2 = AB^2 + AC^2
BC^2 = 15^2 + 3^2
BC^2 = 225 + 9
BC^2 = 234
BC = √234 (approximately 15.297 ft)
Now, we have to determine the height of DE, which is the height difference between D and E.
Since triangles ABC and BDE share an angle at B, they are similar. This means the ratios of corresponding sides are equal.
Using the similar triangles ratio:
AC/BC = DE/BE
Since AC = 3 ft and BC = √234 ft, we can substitute these values:
3/√234 = DE/BE
To solve for DE, we need to find BE.
BE is the horizontal distance between D and E. We can find it by subtracting the length of the ramp from the total distance between A and D:
BE = AD - AB
BE = √(AC^2 + BC^2) - AB
BE = √(3^2 + (√234)^2) - 15
BE = √(9 + 234) - 15
BE ≈ √243 - 15
BE ≈ 15.588 - 15
BE ≈ 0.588 ft
Now we can substitute the values back into the equation:
3/√234 = DE/0.588
To solve for DE, we can cross-multiply:
DE = (3 * 0.588) / √234
DE = 1.764 / 15.297
DE ≈ 0.115 ft
Therefore, the height of the loading dock DE is approximately 0.115 ft.