Thank you. Just a few steps. Doesn't need to be detailed. **Title: Calculating Ladder Length Using the Pythagorean Theorem****Description:**In this problem, we need to determine the length of a ladder required to reach a 25-foot tall house when the ladder is placed 10 feet away from the house.**Problem Statement:**"You need a ladder that will reach up a 25-foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?"To determine the length of the ladder, we can use the Pythagorean Theorem, which applies to right-angled triangles.**Solution:**1. **Identify the triangle:** - The ladder, the distance from the house, and the height of the house form a right-angled triangle. - The distance from the house to the base of the ladder represents one leg of the triangle (10 feet). - The height of the house represents the other leg of the triangle (25 feet). - The ladder represents the hypotenuse of the triangle, which we need to find.2. **Pythagorean Theorem:** The formula is $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, and $a$ and $b$ are the legs of the triangle.3. **Substitute known values:** \[ (10)^2 + (25)^2 = c^2 \] \[ 100 + 625 = c^2 \] \[ 725 = c^2 \]4. **Solve for $c$:** \[ c = \sqrt{725} \] \[ c \approx 26.9 \text{ feet} \]**Conclusion:**The ladder needs to be approximately 26.9 feet long to reach the top of a 25-foot tall house when placed 10 feet away from the house.By understanding and applying the Pythagorean Theorem, you can accurately determine the necessary length of a ladder for any such situation.

This question solve by the method which is given below.

Answered: YOU YOU needa lddder that will reach up…

YOU YOU needa lddder that will reach up a 25 TOot tall house when placed 10 feet away from the house. How tall does the ladder need to be?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Thank you. Just a few steps. Doesn't need to be detailed.

**Title: Calculating Ladder Length Using the Pythagorean Theorem**

**Description:**
In this problem, we need to determine the length of a ladder required to reach a 25-foot tall house when the ladder is placed 10 feet away from the house.

**Problem Statement:**
"You need a ladder that will reach up a 25-foot tall house when placed 10 feet away from the house. How tall does the ladder need to be?"

To determine the length of the ladder, we can use the Pythagorean Theorem, which applies to right-angled triangles.

**Solution:**

1. **Identify the triangle:**
- The ladder, the distance from the house, and the height of the house form a right-angled triangle.
- The distance from the house to the base of the ladder represents one leg of the triangle (10 feet).
- The height of the house represents the other leg of the triangle (25 feet).
- The ladder represents the hypotenuse of the triangle, which we need to find.

2. **Pythagorean Theorem:**
The formula is $a^2 + b^2 = c^2$, where $c$ is the hypotenuse, and $a$ and $b$ are the legs of the triangle.

3. **Substitute known values:**
\[
(10)^2 + (25)^2 = c^2
\]
\[
100 + 625 = c^2
\]
\[
725 = c^2
\]

4. **Solve for $c$:**
\[
c = \sqrt{725}
\]
\[
c \approx 26.9 \text{ feet}
\]

**Conclusion:**
The ladder needs to be approximately 26.9 feet long to reach the top of a 25-foot tall house when placed 10 feet away from the house.

By understanding and applying the Pythagorean Theorem, you can accurately determine the necessary length of a ladder for any such situation.

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