To solve for $x$ in the given right triangle using the Pythagorean theorem, we'll follow these steps:

Step 1: Write down the Pythagorean Theorem

The Pythagorean Theorem states: $a^2 + b^2 = c^2$ where $c$ is the hypotenuse (the side opposite the right angle), and $a$ and $b$ are the other two sides of the triangle.

Step 2: Substitute the known values

In the triangle:

• $a = x$ (the side we need to find)
• $b = 10$
• $c = 20$ (the hypotenuse)

Substituting these values into the theorem: $x^2 + 10^2 = 20^2$

Step 3: Simplify the equation

$x^2 + 100 = 400$

Step 4: Solve for $x^2$

$x^2 = 400 - 100$ $x^2 = 300$

Step 5: Solve for $x$

$x = \sqrt{300}$

Step 6: Simplify the square root and round to the nearest tenth

$x \approx 17.3$

Final Answer

The value of $x$ rounded to the nearest tenth is approximately 17.3.

Would you like more details or have any questions?

Here are five related questions:

1. What is the relationship between the sides of a right triangle?
2. How do you find the length of the hypotenuse if the other two sides are known?
3. How can the Pythagorean theorem be used in three dimensions?
4. What are some common applications of the Pythagorean theorem in real life?
5. How do you determine if a triangle is a right triangle using side lengths?

Tip: Always ensure your calculator is set to the correct mode (degrees or radians) when solving trigonometric problems.