Let's work on the problem labeled 17. This involves solving for $x$ using the Pythagorean theorem since the triangle is a right triangle.

The Pythagorean theorem is expressed as: $a^2 + b^2 = c^2$ where $c$ is the hypotenuse, and $a$ and $b$ are the other two sides of the right triangle.

Step-by-Step Solution:

1. Here:

   • $c = 10$ (hypotenuse),
   • $a = x$ (the unknown side),
   • $b = 2$ (the given leg).

2. Substitute the values into the Pythagorean theorem: $x^2 + 2^2 = 10^2$

3. Simplify: $x^2 + 4 = 100$

4. Subtract 4 from both sides: $x^2 = 96$

5. Solve for $x$ by taking the square root: $x = \sqrt{96}$

6. Simplify the radical: $\sqrt{96} = \sqrt{16 \cdot 6} = 4\sqrt{6}$

Final Answer:

$x = 4\sqrt{6}$

Would you like a detailed explanation or assistance with problem 20?

5 Related Questions:

1. How do you simplify radicals like $\sqrt{96}$ systematically?
2. What are the steps to solve a right triangle when two sides are known?
3. What is the Pythagorean theorem, and how is it applied in real-world problems?
4. Why is simplifying radicals important in mathematical solutions?
5. How can trigonometric functions help solve problems with right triangles?

Tip:

When working with square roots, always look for perfect square factors to simplify the radical efficiently.