https://file.aiquickdraw.com/mathbot/file/1726880351244xzjisw7y.jpg

What is the best option to solve for the missing side 'x'?

The triangle in the image is a right triangle, with legs measuring 15 meters and 12 meters, and the hypotenuse labeled as \(x\). To solve for the missing side \(x\), we can use the **Pythagorean theorem**, which is applied to right triangles and is given by:

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

Where:
- \(a\) and \(b\) are the lengths of the legs of the triangle.
- \(c\) is the length of the hypotenuse (in this case, \(x\)).

Here, \(a = 15\) meters, \(b = 12\) meters, and \(c = x\).

Let's solve for \(x\).

\[
x^2 = 15^2 + 12^2
\]
\[
x^2 = 225 + 144
\]
\[
x^2 = 369
\]
\[
x = \sqrt{369}
\]
\[
x \approx 19.21 \, \text{meters}
\]

Thus, the missing side \(x\) is approximately **19.21 meters**.

Would you like more details or have any other questions?

Here are 5 follow-up questions to explore further:
1. What is the general application of the Pythagorean theorem?
2. How would the solution change if the triangle was not a right triangle?
3. What would happen if one of the other sides was unknown instead?
4. Can you use trigonometric ratios to find angles in the triangle as well?
5. How does the triangle's area change as the side lengths vary?

**Tip:** Always check that the triangle is a right triangle before applying the Pythagorean theorem.

Find the missing side of a right triangle using the Pythagorean theorem. With given legs of 15m and 12m, learn how to calculate the hypotenuse step by step. This solution is suitable for students in Grades 8-10.

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