To solve for the hypotenuse $c$ in a right triangle, you can use the Pythagorean theorem, which states:

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

From the image, you are given:

• $a = 7$
• $b = 24$

Now apply the values into the theorem:

$c^2 = 7^2 + 24^2 = 49 + 576 = 625$

Take the square root of both sides to find $c$:

$c = \sqrt{625} = 25$

So, the length of the hypotenuse is $25$.

Would you like further explanation or have any questions about this process?

Here are 5 related questions you might find useful:

1. How does the Pythagorean theorem apply to non-right triangles?
2. How can you use trigonometry to find the angles in this triangle?
3. What is the difference between the Pythagorean theorem and the distance formula?
4. How do you find the area of a right triangle with known side lengths?
5. How can the Pythagorean theorem be extended to three dimensions?

Tip: Always ensure you know which side is the hypotenuse in a right triangle—the side opposite the right angle!