https://file.aiquickdraw.com/mathbot/file/1728532280604djsn8u24.jpg

The triangle in the image is a right triangle with one leg labeled as 3, the hypotenuse as 7, and the other leg, labeled as \( x \), is the unknown side.

To solve for the missing side \( x \), we can use the **Pythagorean theorem**. The theorem states:

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

where \( c \) is the hypotenuse and \( a \) and \( b \) are the legs of the right triangle.

Given:
- \( c = 7 \) (hypotenuse),
- \( a = 3 \) (one leg),
- \( b = x \) (the missing leg),

We can substitute into the Pythagorean theorem:

\[
3^2 + x^2 = 7^2
\]

This simplifies to:

\[
9 + x^2 = 49
\]

Subtract 9 from both sides:

\[
x^2 = 40
\]

Now, take the square root of both sides:

\[
x = \sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10} \approx 6.32
\]

So, the missing side \( x \) is approximately **6.32** units.

Would you like further details or explanations on any part of the solution?

Here are some related questions to expand on this:

1. How do we determine which side is the hypotenuse in a right triangle?
2. Can you explain how to simplify square roots, like \( \sqrt{40} \)?
3. What are some real-life applications of the Pythagorean theorem?
4. What happens if all three sides of the triangle are unknown?
5. How can we verify that this solution is correct?

**Tip:** Always double-check your solution by plugging it back into the original equation to ensure accuracy!

Identify the missing side in the triangle. One leg is 3, the hypotenuse is 7, and the other leg is unknown (x).

Learn how to find the missing side in a right triangle using the Pythagorean Theorem. This problem involves a triangle with one leg as 3 units, the hypotenuse as 7 units, and the other leg (x) unknown. The solution demonstrates how to apply the Pythagorean Theorem and solve for x, which is approximately 6.32 units.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation