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This is a right triangle with one leg measuring 5.3 units, the hypotenuse measuring 5.9 units, and we are asked to find the length of the missing leg \(x\).

To solve this, we can use the **Pythagorean Theorem**, which states:
\[
a^2 + b^2 = c^2
\]
where:
- \(a\) and \(b\) are the legs of the triangle,
- \(c\) is the hypotenuse.

Given:
- \(a = 5.3\),
- \(c = 5.9\),
- and we need to find \(b = x\).

Substitute the known values into the Pythagorean theorem:
\[
(5.3)^2 + x^2 = (5.9)^2
\]

Now, calculate the squares:
\[
28.09 + x^2 = 34.81
\]

Solve for \(x^2\):
\[
x^2 = 34.81 - 28.09 = 6.72
\]

Finally, take the square root to find \(x\):
\[
x = \sqrt{6.72} \approx 2.6
\]

So, the length of the missing side is approximately \(2.6\) units.

Do you have any questions or need more details?

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Here are five related questions for deeper understanding:
1. What is the Pythagorean theorem used for in right triangles?
2. How do you determine which side is the hypotenuse in a triangle?
3. Can the Pythagorean theorem be applied to non-right triangles?
4. What would happen if the triangle's sides were given in terms of variables?
5. How does rounding affect the final answer in practical problems?

**Tip:** Always double-check which side is the hypotenuse—it is the longest side and opposite the right angle!

Find the missing side of each triangle. Round your answers to the nearest tenth if necessary.

Learn how to solve for the missing side of a right triangle using the Pythagorean Theorem. This example problem involves a triangle with legs of 5.3 units, a hypotenuse of 5.9 units, and asks you to find the length of the unknown leg. Suitable for students in Grades 8-10.

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