Fill in the blanks!

To fill in the blanks for the given triangle, we will assume you're solving for the missing side \( a \) using the Pythagorean theorem. The triangle has one side of \( \sqrt{62} \) inches, another side of \( 6 \) inches, and we need to find the missing side \( a \).

We can identify \( \sqrt{62} \) as the hypotenuse and \( 6 \) as one of the legs of the triangle.

Using the Pythagorean theorem:

\[ a^2 + b^2 = c^2 \]

where:

• \( a \) is the length of one leg (unknown),
• \( b = 6 \) inches is the length of the other leg,
• \( c = \sqrt{62} \) inches is the hypotenuse.

Now we can fill in the equations step by step using the values provided:

1. Starting with: \[ a^2 + b^2 = c^2 \] Filling in the known values: \[ a^2 + 6^2 = (\sqrt{62})^2 \]

2. Now substitute the squares: \[ a^2 + 36 = 62 \]

3. Next, solve for \( a^2 \): \[ a^2 = 62 - 36 \] \[ a^2 = 26 \]

4. Finally, take the square root: \[ \sqrt{a^2} = \sqrt{26} \]

Now, we can fill in the respective blanks:

1. a^(2) + 6^(2) = (\sqrt{62})^(2)
2. a^(2) + 6^(2) = (\sqrt{62})^(2)
3. a^(2) + 36 = 62
4. a^(2) = 26
5. \sqrt{a^2} = \sqrt{26}
6. a = \sqrt{26} in.

So the blanks can be filled as follows:

1. 6
2. 6
3. 36
4. 26
5. 26

Thus, the complete set of filled equations is:

• a^(2) + 6^(2) = (\sqrt{62})^(2)
• a^(2) + 6^(2) = 62
• a^(2) + 36 = 62
• a^(2) = 26
• \sqrt(a^(2)) = \sqrt{26}
• a = \sqrt{26} in.