To solve for $b$ in the given triangle, we will use the Pythagorean Theorem, which states:

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

Here:

• $a = 2$
• $c = \sqrt{5}$

Substitute these values into the equation:

$2^2 + b^2 = (\sqrt{5})^2$

Simplify:

$4 + b^2 = 5$

Isolate $b^2$:

$b^2 = 5 - 4$

$b^2 = 1$

Take the square root of both sides:

$b = \sqrt{1} = 1$

Thus, the value of $b$ is 1.

Would you like further clarification? Here are some related questions for better understanding:

1. How does the Pythagorean Theorem apply to different types of triangles?
2. What are some common mistakes to avoid when solving for missing sides?
3. How do you simplify square roots when the answer is not an integer?
4. How would this solution change if the given values included decimals?
5. Can the Pythagorean Theorem be used for 3D problems?

Tip: Always double-check whether the triangle is a right triangle before using the Pythagorean Theorem.