To find the hypotenuse of a right triangle when the lengths of the legs are given, you can use the Pythagorean theorem:

$c = \sqrt{a^2 + b^2}$

Where:

• $a = 12$
• $b = 15$

Substitute the values into the formula:

$c = \sqrt{12^2 + 15^2}$

$c = \sqrt{144 + 225}$

$c = \sqrt{369}$

Now, calculate the square root of 369:

$c \approx 19.2$

So, the hypotenuse is approximately 19.2.

Would you like further details, or do you have any other questions?

Here are some related questions for further exploration:

1. How do you find the length of a missing leg in a right triangle if the hypotenuse and one leg are given?
2. What is the relationship between the sides of a right triangle in the Pythagorean theorem?
3. Can the Pythagorean theorem be used for triangles that are not right triangles?
4. How do you determine if a triangle is a right triangle using its side lengths?
5. What are the properties of a 30-60-90 triangle?
6. How would you solve for the hypotenuse if the triangle's legs were in different units (e.g., cm and inches)?
7. What is the geometric interpretation of the Pythagorean theorem?
8. How can the Pythagorean theorem be applied in three-dimensional space?

Tip: The Pythagorean theorem is a foundational concept in geometry, and understanding it thoroughly can be beneficial for solving a variety of problems involving right triangles.