Solve Trig Problem: Horizontal Dist. Between Truck & Dock to Nearest Tenth

• Liam C
In summary, the conversation discusses how to find the horizontal distance between the back of a truck and a loading dock, given the length of the loading ramp and the heights of the dock and truck. The conversation includes a suggested solution using a right triangle and the Pythagorean theorem, but the expert summarizer points out an error in the calculation and suggests a simpler approach using only the truck, ramp, and dock without involving the ground.
Liam C

Homework Statement

A loading ramp is 2.8m long. One end rests on a loading dock 0.7 meters above the ground, and the other end leads into the back of a a tractor trailer 1.2m above the ground. Find the horizontal distance between the back of the truck and the loading dock, to the nearest tenth of a meter.

a² + b² = c²

The Attempt at a Solution

In order to solve this problem I figured out that you need to make an imaginary hypotenuse from the ground below the truck to the top of the loading dock. With that hypotenuse you need to figure out the horizontal distance between the back of the truck and the loading dock.
Attempt:
Let x represent the diagonal from the ground at the truck to the loading dock.
2.8^2 - .7^2 = x^2
√6.4 = √x^2
2.53m = x
That is for the imaginary hypotenuse. Now for the leg it asked for:
Let h represent the horizontal distance between the back of the truck to the start of the dock.
2.53^2 - .7^2 = h^2
6.4 - .49 = h^2
√5.91 = √h^2
2.43m = h
Then the therefor statement. The problem is, the textbook tells me the answer is 2.8. Where did I go wrong?
P.S
To get a mental image, just imagine a rectangle with a diagonal from the lower left corner to the upper right corner.

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What do you need the ground and this imaginary hypotenuse for? Have you drawn the situation?

fresh_42 said:
What do you need the ground and this imaginary hypotenuse for? Have you drawn the situation?
Yes, I have drawn it. You need the hypotenuse because the length it is asking me to solve requires it.
https://www.physicsforums.com/attachments/101935

Last edited by a moderator:
So you want to find ##h##. But ##h## can also be found at another place. This should simplify your calculation. Maybe you see it better, if you only think of the truck, the ramp and the dock. You don't need the ground.

Edit: Your error is that you apply Pythagoras on a triangle which isn't a right one.

Liam C
fresh_42 said:
So you want to find ##h##. But ##h## can also be found at another place. This should simplify your calculation. Maybe you see it better, if you only think of the truck, the ramp and the dock. You don't need the ground.

Edit: Your error is that you apply Pythagoras on a triangle which isn't a right one.
Ohhh, okay I think I can solve it from here, thank you.

1. What is a trigonometry problem?

A trigonometry problem is a mathematical equation or scenario that involves using the principles of trigonometry, which is a branch of mathematics that deals with the relationships between the sides and angles of triangles. These problems often involve finding missing angles or sides, or solving for a specific variable.

2. Why is it important to solve trigonometry problems?

Trigonometry is used in various fields such as engineering, physics, and astronomy. Solving trigonometry problems can help us understand and analyze real-world situations, make accurate calculations, and solve complex problems.

3. What is the horizontal distance between a truck and a dock in a trigonometry problem?

The horizontal distance is the distance between the truck and the dock when viewed from a bird's eye view, assuming that the truck and dock are at the same height. This distance is often represented by the variable x in trigonometry problems.

4. How do you find the horizontal distance in a trigonometry problem?

To find the horizontal distance, you need to use the trigonometric ratio known as cosine (cos). In a right triangle, cosine is equal to the adjacent side over the hypotenuse. So, if you know the angle between the truck and the dock and the length of the adjacent side (usually the height of the truck), you can use cos to calculate the horizontal distance.

5. Why is the horizontal distance rounded to the nearest tenth in trigonometry problems?

In real-world scenarios, measurements are often not exact, and there may be some level of uncertainty. Rounding the horizontal distance to the nearest tenth helps to account for this uncertainty and provide a more realistic and practical answer.

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