We are solving the equation:

$C = \sqrt{a^2 - b^2}$

where:

• $C = 10$,
• $b = 6$,
• $a > 0$.

Step 1: Substitute the values of $C$ and $b$ into the equation

$10 = \sqrt{a^2 - 6^2}$

Step 2: Simplify the expression

$10 = \sqrt{a^2 - 36}$

Step 3: Square both sides to eliminate the square root

$10^2 = a^2 - 36$ $100 = a^2 - 36$

Step 4: Solve for $a^2$

$a^2 = 100 + 36$ $a^2 = 136$

Step 5: Solve for $a$

Since $a > 0$: $a = \sqrt{136}$ Simplify the square root: $a = \sqrt{4 \cdot 34} = 2\sqrt{34}$

Thus, the positive value of $a$ is: $a = 2\sqrt{34} \approx 11.66$

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Would you like additional details about the steps? Here are five related questions for further exploration:

1. How do you simplify square roots, such as $\sqrt{136}$?
2. What happens if $a$ were negative in this context?
3. Can you generalize this solution for other values of $C$ and $b$?
4. How do you solve equations involving square roots in general?
5. What are the applications of this formula in physics or geometry?

Tip: Always check your calculations when squaring or simplifying square roots to avoid errors!