To solve the equation \(182 + b^2 = 302\), we first isolate \(b^2\):
\[ b^2 = 302 - 182 \] \[ b^2 = 120 \]
Next, we find \(b\) by taking the square root of both sides:
\[ b = \sqrt{120} \approx 10.95 \]
This calculated length \(b\) represents one of the legs of a right triangle if we consider the equation in the context of the Pythagorean theorem, which states \(a^2 + b^2 = c^2\) (where \(c\) is the hypotenuse).
To identify \(a\) and \(c\), we can check the values noted in the responses:
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If the triangle has legs of lengths 30 and 24:
- The hypotenuse would be calculated as: \[ c^2 = 30^2 + 24^2 = 900 + 576 = 1476 \]
- The hypotenuse \(c\) would be \(c = \sqrt{1476} \approx 38.4\).
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The responses about the hypotenuse being 18, or with missing side lengths of 34.99 and 24, do not directly follow from our earlier calculations.
Hence, the closest matching statement to what's derived from the equation is:
The triangle is a right triangle with a missing leg length of approximately 10.95, not included in the provided responses directly.
It seems that none of the responses match perfectly with our derived information, but among the choices:
- Based on \(b^2 = 120\) implying one leg’s possible computations, the answer closest could be interpreted as the triangle having legs that sum my calculations of potential leg values; however, this wasn't offered in your responses.
From the explicit choices given, the choice "The triangle is a right triangle, and the legs are 30 and 24" does appear accurate—yet this would not logically align with what we derived from the equation given.
Thus, there is a mismatch between the direct analysis versus provided options.