Answer:
![x = √(57)](https://img.qammunity.org/2023/formulas/mathematics/high-school/kxi6ejy5j6utv33rd1qlay70z94qrfwwo2.png)
Explanation:
The Pythagorean Theorem states that:
![a^2 + b^2 = c^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/3gmi15x8fo87zd30pqhytr7xqz9u9fgnja.png)
where
and
are legs of a right triangle (they meet at the right angle), and
is the triangle's hypotenuse.
We can apply this theorem to the given triangle:
,
and all we have to do is solve for x.
First, simplify all the square roots.
![64 + x^2 = 121](https://img.qammunity.org/2023/formulas/mathematics/high-school/qqj3ouh5fkm0s7xoutq3wtduuy9pa2n7ru.png)
Then, subtract 64 from both sides.
![x^2 = 121- 64](https://img.qammunity.org/2023/formulas/mathematics/high-school/pa89lzs2ryboskph20rnqr7e5zwmrzro1z.png)
![x^2 = 57](https://img.qammunity.org/2023/formulas/mathematics/high-school/94g5abtvjkfdvhe9qp2rnkd167dkproine.png)
Finally, take the square root of both sides.
![√(x^2) = √(57)](https://img.qammunity.org/2023/formulas/mathematics/high-school/ti2xu9xtfnlqkiqkhdd381c63wjsf3ysos.png)
![x = √(57)](https://img.qammunity.org/2023/formulas/mathematics/high-school/kxi6ejy5j6utv33rd1qlay70z94qrfwwo2.png)