To solve for the missing side of the right triangle, we use the Pythagorean Theorem:

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

• $c$ is the hypotenuse (given as $\sqrt{116}$),
• $a$ and $b$ are the two legs (one leg is 10, and the other is unknown).

Step 1: Substituting known values

Here:

• $a = 10$,
• $c = \sqrt{116}$.

The equation becomes:

$10^2 + b^2 = (\sqrt{116})^2$

Step 2: Simplify the equation

1. $10^2 = 100$,
2. $(\sqrt{116})^2 = 116$.

So:

$100 + b^2 = 116$

Step 3: Solve for $b^2$

Subtract 100 from both sides:

$b^2 = 116 - 100$ $b^2 = 16$

Step 4: Solve for $b$

Take the square root of both sides:

$b = \sqrt{16} = 4$

Final Answer:

The missing side length is 4.

Would you like me to provide further explanations or verify any steps? Let me know!

Related Questions:

1. What is the Pythagorean Theorem, and why does it work?
2. How do you find the hypotenuse if two legs are given?
3. How do you simplify expressions involving square roots?
4. What happens if the triangle's sides are decimals or fractions?
5. Can the Pythagorean Theorem be extended to 3D shapes?

Tip: The Pythagorean Theorem only works for right triangles! Always confirm the triangle's angles first.