for the following right triangle find the side length x

Guri Bee

less than a minute read

·

20-10-2024

1

0

Share

Solving for the Missing Side in a Right Triangle: A Step-by-Step Guide

Understanding how to find missing side lengths in a right triangle is a fundamental concept in geometry. This article will guide you through the process using the Pythagorean theorem and explore practical examples.

The Problem:

Let's say we have a right triangle with sides of length 3 and 4. We need to find the length of the hypotenuse, denoted by 'x'.

Solution:

The Pythagorean theorem states: "In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides."

Mathematically, this is expressed as:

a² + b² = c²

Where:

• a and b are the lengths of the two shorter sides (legs) of the right triangle
• c is the length of the hypotenuse

Applying the Theorem to our Problem:

1. Identify the sides: We have a = 3 and b = 4.
2. Substitute the values into the equation: 3² + 4² = x²
3. Simplify: 9 + 16 = x²
4. Combine the terms: 25 = x²
5. Solve for x: x = √25 = 5

Therefore, the length of the hypotenuse (x) is 5.

Practical Applications:

The Pythagorean theorem has wide applications in various fields, including:

• Construction: Calculating the length of diagonal supports for roofs and bridges.
• Navigation: Determining distances between points on a map.
• Engineering: Designing structures like buildings and machines.

Example:

Imagine you're building a ramp with a horizontal length of 12 feet and a vertical height of 5 feet. To determine the length of the ramp itself, you would use the Pythagorean theorem.

1. a = 12 (horizontal length)
2. b = 5 (vertical height)
3. c = ramp length (hypotenuse)

Substituting these values into the equation:

12² + 5² = c² 144 + 25 = c² 169 = c² c = √169 = 13

Therefore, the ramp needs to be 13 feet long.

Conclusion:

The Pythagorean theorem provides a powerful tool for calculating missing side lengths in right triangles. It has numerous practical applications across various fields. By understanding the theorem and its application, you can solve real-world problems and gain a deeper appreciation for the principles of geometry.