Due To Storm, A Tree Breaks At A Height Of 8m From The Ground And Its Top Touches The Ground At A Distance Of 15m From The Base Of The Tree. Answer The Following Questions. A) Find The Original Height Of The Tree. B) Find The Difference Between The

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Introduction

In this problem, we are presented with a scenario where a tree breaks due to a storm, and its top touches the ground at a distance of 15m from the base of the tree. The height at which the tree breaks is given as 8m from the ground. Our objective is to find the original height of the tree and the difference between the original height and the height at which the tree breaks.

Problem Formulation

Let's denote the original height of the tree as h and the distance from the base of the tree to the point where the tree breaks as x. We are given that the height at which the tree breaks is 8m, so we can write:

h - 8 = x

We are also given that the distance from the base of the tree to the point where the tree touches the ground is 15m. Since the tree breaks at a height of 8m, the distance from the point where the tree breaks to the ground is also 15m. Therefore, we can write:

x + 8 = 15

Solving the Problem

Now, we can solve the system of equations to find the original height of the tree.

Step 1: Solve for x

We can solve the second equation for x:

x = 15 - 8 x = 7

Step 2: Find the original height of the tree

Now that we have the value of x, we can substitute it into the first equation to find the original height of the tree:

h - 8 = 7 h = 15

Therefore, the original height of the tree is 15m.

Answer to Question a)

The original height of the tree is 15m.

Answer to Question b)

The difference between the original height and the height at which the tree breaks is:

15 - 8 = 7m

Therefore, the difference between the original height and the height at which the tree breaks is 7m.

Conclusion

In this problem, we used basic algebraic techniques to solve a system of equations and find the original height of the tree. We also calculated the difference between the original height and the height at which the tree breaks. This problem demonstrates the importance of using mathematical techniques to analyze and solve real-world problems.

Mathematical Concepts Used

  • Algebraic equations
  • System of equations
  • Solving for variables
  • Basic arithmetic operations (addition, subtraction, multiplication, division)

Real-World Applications

This problem has real-world applications in various fields, such as:

  • Forestry: Understanding the height of trees is crucial for forestry management, including tree planting, pruning, and harvesting.
  • Architecture: Knowing the height of trees is essential for designing buildings and structures that are safe and aesthetically pleasing.
  • Environmental Science: Understanding the height of trees is important for studying the impact of climate change on tree growth and distribution.

Further Reading

For more information on algebraic equations and system of equations, please refer to the following resources:

  • Khan Academy: Algebraic Equations
  • Mathway: System of Equations
  • Wolfram MathWorld: Algebraic Equations
    9. Due to Storm, a Tree Breaks: A Mathematical Analysis ===========================================================

Q&A: Frequently Asked Questions

Q: What is the original height of the tree?

A: The original height of the tree is 15m.

Q: What is the height at which the tree breaks?

A: The height at which the tree breaks is 8m.

Q: What is the distance from the base of the tree to the point where the tree breaks?

A: The distance from the base of the tree to the point where the tree breaks is 7m.

Q: What is the difference between the original height and the height at which the tree breaks?

A: The difference between the original height and the height at which the tree breaks is 7m.

Q: How do I calculate the original height of the tree?

A: To calculate the original height of the tree, you can use the following steps:

  1. Write an equation representing the height at which the tree breaks: h - 8 = x
  2. Write an equation representing the distance from the base of the tree to the point where the tree touches the ground: x + 8 = 15
  3. Solve the second equation for x: x = 15 - 8
  4. Substitute the value of x into the first equation: h - 8 = 7
  5. Solve for h: h = 15

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in various fields, such as:

  • Forestry: Understanding the height of trees is crucial for forestry management, including tree planting, pruning, and harvesting.
  • Architecture: Knowing the height of trees is essential for designing buildings and structures that are safe and aesthetically pleasing.
  • Environmental Science: Understanding the height of trees is important for studying the impact of climate change on tree growth and distribution.

Q: What mathematical concepts are used in this problem?

A: This problem uses the following mathematical concepts:

  • Algebraic equations
  • System of equations
  • Solving for variables
  • Basic arithmetic operations (addition, subtraction, multiplication, division)

Q: How can I practice solving problems like this?

A: You can practice solving problems like this by:

  • Working through example problems in your textbook or online resources
  • Practicing with online math tools and calculators
  • Joining a study group or math club to work with others on math problems
  • Seeking help from a teacher or tutor if you need additional support

Conclusion

In this Q&A article, we have answered some of the most frequently asked questions about the problem of a tree breaking due to a storm. We have also provided additional resources and tips for practicing and mastering the mathematical concepts used in this problem.