A 17 -foot ladder is leaning on a tree. The bottom of the ladder on the ground at a distance of 4 feet from the base of the tree. The base of the tree and the ground form a right angle as shown.

This problem involves a right triangle formed by the ladder, the tree, and the ground. We can use the Pythagorean theorem to find the height at which the ladder touches the tree.

The Pythagorean theorem is:

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

Where:
- \(a\) is the distance from the base of the tree to the bottom of the ladder (4 feet),
- \(b\) is the height where the ladder touches the tree (which we need to find),
- \(c\) is the length of the ladder (17 feet).

Substitute the known values into the equation:

\[
4^2 + b^2 = 17^2
\]

\[
16 + b^2 = 289
\]

Now, subtract 16 from both sides:

\[
b^2 = 289 - 16 = 273
\]

Take the square root of both sides:

\[
b = \sqrt{273} \approx 16.52 \, \text{feet}
\]

So, the ladder touches the tree at approximately **16.52 feet** above the ground.

Would you like more details or have any questions?

Here are 5 related questions to extend this concept:
1. What is the angle formed between the ladder and the ground?
2. How would the height change if the distance from the base of the tree to the ladder increased?
3. If the ladder were 20 feet long, what would the new height be?
4. How does this problem relate to trigonometric functions like sine or cosine?
5. What would happen if the ground were sloped instead of flat?

**Tip:** When solving problems involving right triangles, always check if the Pythagorean theorem can simplify the calculations.

A 17-foot ladder is leaning on a tree. The bottom of the ladder is on the ground at a distance of 4 feet from the base of the tree. The base of the tree and the ground form a right angle as shown.

This solution demonstrates how to calculate the height at which a 17-foot ladder touches a tree when its base is 4 feet away from the tree using the Pythagorean Theorem. The problem involves a right triangle formed by the ladder, the ground, and the tree, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation