The image shows a right triangle with one leg labeled as $x$, the other leg labeled as 8, and the hypotenuse labeled as 14. The task is to find the missing side $x$ using the Pythagorean theorem.

Pythagorean Theorem

The Pythagorean theorem states that in a right triangle: $a^2 + b^2 = c^2$ where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse.

Given:

• One leg $a = 8$
• Hypotenuse $c = 14$
• Other leg $b = x$

Solution:

We need to solve for $x$ using the equation: $8^2 + x^2 = 14^2$

1. Calculate $8^2$: $8^2 = 64$

2. Calculate $14^2$: $14^2 = 196$

3. Substitute the values into the equation: $64 + x^2 = 196$

4. Solve for $x^2$: $x^2 = 196 - 64 = 132$

5. Take the square root of both sides: $x = \sqrt{132}$

6. Simplify the square root: $x = \sqrt{4 \times 33} = 2\sqrt{33} \approx 11.49$

So, the missing side $x$ is approximately $11.49$ units.

Would you like further details or have any questions?

Relative Questions:

1. How would you solve for $x$ if the given triangle had different side lengths?
2. What is the significance of the Pythagorean theorem in geometry?
3. Can the Pythagorean theorem be applied to non-right triangles?
4. How do you simplify square roots like $\sqrt{132}$?
5. What are some real-life applications of the Pythagorean theorem?

Tip:

Always check if a given triangle is a right triangle before applying the Pythagorean theorem.