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The problem in the image describes a right triangle formed by a 10-foot ladder leaning against a tree. The bottom of the ladder is 7 feet away from the base of the tree, and we are asked to find the vertical distance between the ground and the top of the ladder.

This problem can be solved using the **Pythagorean Theorem**, which is:

\[
a^2 + b^2 = c^2
\]

Where:
- \(a\) is the distance from the base of the tree to the bottom of the ladder (7 feet),
- \(b\) is the height from the ground to the top of the ladder (this is the unknown we need to find),
- \(c\) is the length of the ladder (10 feet).

Substitute the known values:

\[
7^2 + b^2 = 10^2
\]

\[
49 + b^2 = 100
\]

Now, solve for \(b\):

\[
b^2 = 100 - 49
\]

\[
b^2 = 51
\]

\[
b = \sqrt{51} \approx 7.14 \text{ feet}
\]

So, the height of the ladder from the ground to the top is approximately **7.1 feet**, rounded to the nearest tenth.

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Do you want more details or have any questions?

Here are five questions related to this problem:
1. How is the Pythagorean Theorem useful in real-life applications?
2. What are the conditions for using the Pythagorean Theorem?
3. What would happen if the ladder were longer than 10 feet?
4. How would you solve for the distance if the angle between the ladder and the ground was known?
5. Can this problem be solved using trigonometry? If so, how?

**Tip**: In any right triangle problem, always verify that you are working with a right angle, so the Pythagorean Theorem applies!

A 10-foot ladder is leaning on a tree. The bottom of the ladder on the ground is at a distance of 7 feet from the base of the tree. The base of the tree and the ground form a right angle. What is the distance, in feet, between the ground and the top of the ladder? Round your answer to the nearest tenth.

Learn how to use the Pythagorean Theorem to find the height of a ladder leaning on a tree. In this problem, a 10-foot ladder leans against a tree, with the bottom of the ladder 7 feet from the base. The solution uses the Pythagorean Theorem to find the vertical distance. Suitable for students in Grades 7-9.

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