Question

Fill in the blanks!

Pythagorean theorem: a^(2) + b^(2) = c^(2)
a^(2) + _ = _^(2)
a^(2) + _ = 841
a^(2) = _ - 484
a^(2) = _
\sqrt(a^(2) = \sqrt(357)
a = \sqrt(_) m

Answer 1

Let's fill in the blanks step by step.

1. Pythagorean theorem: a^(2) + b^(2) = c^(2)
- Here, _ = b^(2) and _ = c

2. a^(2) + _ = 841
- This means _ = b^(2)

3. a^(2) = _ - 484
- Here, we can substitute _ = 841, so:
- a^(2) = 841 - 484

4. Calculate a^(2):
- a^(2) = 841 - 484 = 357

5. Therefore, a^(2) = 357.

6. Now, substitute into the last equation:
- \(\sqrt{a^{2}} = \sqrt{357}\)

7. Finally, to find a:
- a = \(\sqrt{357}\) m

So, the filled-in blanks are:

Pythagorean theorem: a^(2) + b^(2) = c^(2)
a^(2) + **b^(2)** = **c**^(2)
a^(2) + **484** = **841**
a^(2) = **841** - 484
a^(2) = **357**
√a^(2) = √(357)
a = √(**357**) m