https://file.aiquickdraw.com/mathbot/file/1727971733836vnv8v0nv.jpg

The image shows a right triangle where one leg is 5, another leg is 8, and you are asked to find the hypotenuse \(x\).

We can use the **Pythagorean theorem** to solve this, which states that in a right triangle:

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

Where:
- \(x\) is the hypotenuse (the side opposite the right angle, which we need to find),
- \(a = 5\) and \(b = 8\) are the two legs of the triangle.

Let's calculate \(x\):

\[
x^2 = 5^2 + 8^2 = 25 + 64 = 89
\]

Now, take the square root of both sides to find \(x\):

\[
x = \sqrt{89} \approx 9.43
\]

So, the value of \(x\) is approximately **9.43**.

Would you like a more detailed breakdown of the steps?

Here are some related questions to explore:
1. What are the conditions for using the Pythagorean theorem?
2. Can the Pythagorean theorem be applied to non-right triangles?
3. How can we verify the accuracy of the square root calculation for \(x\)?
4. What are some real-life applications of the Pythagorean theorem?
5. How would the solution change if the triangle were scaled?

**Tip:** When working with right triangles, the Pythagorean theorem is a powerful tool to solve for missing sides as long as the triangle has a right angle.

Find x in the right triangle where one leg is 5, the other leg is 8, and x is the hypotenuse.

Learn how to find the hypotenuse of a right triangle using the Pythagorean Theorem. In this example, the triangle has legs of 5 and 8, and the solution involves applying the formula x^2 = a^2 + b^2. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation