To analyze the equation \(182 + b^2 = 302\):
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We can rearrange it to find \(b^2\): \[ b^2 = 302 - 182 \] \[ b^2 = 120 \]
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Now, taking the square root to find \(b\): \[ b = \sqrt{120} \approx 10.95 \]
Now, knowing this, we need to consider the context of a triangle. If we are working with the Pythagorean theorem, where \(a^2 + b^2 = c^2\), we can assume:
- \(182\) corresponds to one leg of the triangle, which is \(30^2 = 900\) (because \(30^2 = 900\), correcting our understanding of the values}
- \(b^2\) will correspond to another leg, which we calculated to be approximately \(10.95^2\)
- The hypotenuse squared can then be \(c^2 = 302\).
However, \(b\) itself wasn't a leg or hypotenuse until we calculate and see what fits.
Given the options provided, the calculation actually leads us to conclude that:
- The triangle is a right triangle with one leg approximately \(10.95\) when added to the square of \(30^2 (900) = 302\ approx~ 10.95\), which does not seem listed.
But the questions or options presented in the responses do not fit this outcome directly. The calculations were leading back to not being able to satisfy matches within the given options of:
- 34.99
- 24
- 30 & 24
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We confirm that \(b\) doesn't fit the hypothesis from above.
So, if you are considering a right triangle with options, ensure which values belong accurately or specify a further direction to what you're deriving from those calculations.
None of the listed answer choices directly follow from the calculation presented. Would you need more criteria or data?