To find the length of the hypotenuse $AB$ of the right triangle $ABC$, we can apply the Pythagorean Theorem, which states:

$c^2 = a^2 + b^2$

where $c$ is the hypotenuse and $a$ and $b$ are the other two sides.

From the diagram, the two legs of the triangle $ABC$ are given as:

• $AC = 6$
• $AB = 5$

We can substitute these values into the Pythagorean theorem:

$AB^2 = AC^2 + BC^2$

$AB^2 = 6^2 + 5^2 = 36 + 25 = 61$

Taking the square root of both sides:

$AB = \sqrt{61} \approx 7.81$

So, the correct length of the hypotenuse is approximately 7.8, but none of the choices exactly match this. The closest approximation from the given options is C) 7.2.

Would you like further details on this?

Here are some related questions to explore:

1. What is the exact value of $\sqrt{61}$?
2. How does the Pythagorean theorem apply to different triangles?
3. Can the sides of a right triangle always be integers?
4. How do we verify if a triangle is a right triangle using side lengths?
5. What are the implications of rounding when calculating geometric values?

Tip: When solving with the Pythagorean theorem, ensure that you correctly identify the two legs and the hypotenuse!