To solve for the missing side $c$ (the hypotenuse) of the right triangle using the Pythagorean Theorem, the equation is:

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

where:

• $a = 5 \, \text{cm}$ (one leg),
• $b = 12 \, \text{cm}$ (the other leg),
• $c$ is the hypotenuse.

Steps:

1. Substitute the values of $a$ and $b$ into the equation: $5^2 + 12^2 = c^2$

2. Calculate the squares: $25 + 144 = c^2$

3. Add the results: $169 = c^2$

4. Solve for $c$ by taking the square root of both sides: $c = \sqrt{169}$

5. Simplify: $c = 13$

Final Answer:

The missing side $c$ (the hypotenuse) is 13 cm.

Would you like a breakdown of the Pythagorean Theorem or examples for different triangle problems?

Related Questions:

1. What is the Pythagorean Theorem, and when is it used?
2. How do you find a missing leg if the hypotenuse and one side are known?
3. How can you prove the Pythagorean Theorem geometrically?
4. What are Pythagorean triples, and how are they useful?
5. How do you apply the Pythagorean Theorem in real-life problems?

Tip: Always ensure the triangle is a right triangle before applying the Pythagorean Theorem.