To solve the equation \(182 + b^2 = 302\), we can rearrange it to find \(b^2\).
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Subtract 182 from both sides: \[ b^2 = 302 - 182 \] \[ b^2 = 120 \]
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Next, we take the square root of both sides to find \(b\): \[ b = \sqrt{120} \approx 10.95 \]
However, the problem appears to relate to a right triangle scenario where \(182\) corresponds to one leg, \(b\) corresponds to the missing leg, and the total of \(302\) represents the square of the hypotenuse. Let's evaluate this further assuming \(182\) represents a leg and \(302\) the hypotenuse squared.
Using the Pythagorean theorem: \[ a^2 + b^2 = c^2 \]
Here, let \(a^2 = 182\), and assume \(c^2 = 302\) for the hypotenuse. We found \(b^2 = 120\).
Using the lengths,
- \(a = \sqrt{182} \approx 13.5\)
- \(b = \sqrt{120} \approx 10.95\)
- And the hypotenuse \(c = \sqrt{302} \approx 17.35\)
From the given responses, we realize that none of the provided options directly mention being able to derive a side length of 24 in the context provided. However, the closest correct identification is regarding the triangle's properties given the newfound lengths. None of the multiple choices match our calculated leg lengths specifically; thus, based on our computation:
- The missing leg's approximate length is about 10.95, not matching the 24 or 34.99.
- The hypotenuse (root of 302) is approximately 17.35, which also doesn't directly fit the description.
So the best understanding we can gather from the original problem is that we have a right triangle with approximate side lengths but none of the provided specific options completely correspond to our calculations.
In conclusion, if needing to select an answer based on given content, none accurately reflect our findings for \(b\). However, to the essence of the problem, one might argue for the triangle's relationship indicated as a right-angled triangle established by calculations irrespective of exact length being noted.