The ramp shown below is used to move crates of oranges to loading docks at diffrent heights. When the horizontal distance ab is 15 feet the height of the loading dock, bc ,is 3 feet. What is the height?
A) 5 feet
B) 8 feet
C) 9 feet
D) 25 feet
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Please help me I need this ASAP like RIGHT now it would be so highly appreciated as my grades are decent and I dont want them to slip
3^2 + h^2 = 15^2
To find the height of the loading dock, we can use the concept of similar triangles.
In the given ramp, we have two triangles: triangle ABC and triangle ABD.
- Triangle ABC represents the ramp.
- Triangle ABD represents the loading dock and the ramp combined.
We know that corresponding sides of similar triangles are proportional. Therefore, we can set up the following proportion:
AD/AB = BD/BC
Let's substitute the given values:
AD/15 = BD/3
We are looking for the height of the loading dock, so let's solve for AD.
Cross-multiplying the equation, we get:
3 * AD = 15 * BD
Simplifying the equation:
AD = 5 * BD
From this equation, we can see that the height of the loading dock (AD) is 5 times the height of the ramp (BD).
Now, let's look at the given answer options:
A) 5 feet
B) 8 feet
C) 9 feet
D) 25 feet
We can calculate the height using the ratio mentioned above:
If BD (height of the ramp) is 1 foot, then AD (height of the loading dock) would be 5 feet (1 foot multiplied by 5).
Comparing the answer options, we can see that the height of the loading dock is equal to 5 times the height of the ramp, which means the correct answer is:
A) 5 feet.
Therefore, the height of the loading dock is 5 feet.