To determine the value of $b$ in the given right triangle, we will use the Pythagorean Theorem:

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

• $c$ is the hypotenuse,
• $a$ is one leg,
• $b$ is the other leg.

Step-by-Step Solution:

1. Substitute the known values $a = 5$ and $c = 20$ into the equation: $20^2 = 5^2 + b^2$

2. Simplify the squares: $400 = 25 + b^2$

3. Solve for $b^2$ by subtracting 25 from both sides: $b^2 = 400 - 25$ $b^2 = 375$

4. Take the square root of both sides to find $b$: $b = \sqrt{375}$

5. Simplify the square root (using a calculator for precision): $b \approx 19.36$

Final Answer:

The value of $b$ is approximately 19.36 (rounded to two decimal places).

Let me know if you want further clarifications or details!

Related Questions:

1. How do you use the Pythagorean Theorem to solve for missing triangle sides?
2. What is the difference between right triangles and other types of triangles?
3. How can trigonometry be used to solve for angles in this triangle?
4. If angle $A$ is required, how do you calculate it using trigonometric ratios?
5. What is the general formula for calculating the hypotenuse in a right triangle?

Tip:

In right triangles, Pythagoras' Theorem is a fundamental tool for solving missing side lengths when two sides are known.