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?

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!