Let's fill in the blanks step by step.
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Pythagorean theorem: a^(2) + b^(2) = c^(2)
- Here, _ = b^(2) and _ = c
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a^(2) + _ = 841
- This means _ = b^(2)
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a^(2) = _ - 484
- Here, we can substitute _ = 841, so:
- a^(2) = 841 - 484
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Calculate a^(2):
- a^(2) = 841 - 484 = 357
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Therefore, a^(2) = 357.
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Now, substitute into the last equation:
- \(\sqrt{a^{2}} = \sqrt{357}\)
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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