To determine the properties of the triangle based on the equation \( 182 + b^2 = 302 \), we can first solve for \( b^2 \):
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Subtract 182 from both sides of the equation: \[ b^2 = 302 - 182 \] \[ b^2 = 120 \]
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Taking the square root of both sides gives: \[ b = \sqrt{120} \approx 10.95 \]
Now, since the equation resembles the Pythagorean theorem \( a^2 + b^2 = c^2 \), we can infer that \( 18 \) is the hypotenuse because \( 18^2 = 324 \), which is consistent with the equation set up.
However, none of the given choices directly correspond to this \( b \) value, and there's also an indication that the triangle's hypotenuse or leg lengths do not match exactly with our findings.
Considering that we deduced hypotenuse is \( 18 \) and one leg calculated approximately \( 10.95 \), \( a^2 = 182 \) leads to:
- The other leg of the triangle would be: \[ a = \sqrt{182} \approx 13.45 \]
However, \( 30 \) and \( 24 \) do not fit with this analysis either, but here we can conclude based on the calculation that:
The triangle is a right triangle, but we do not have the exact values of legs being \( 30 \), \( 24 \), or any mentioned \( 34.99 \) in conclusion.
Therefore, none of the options exactly fits, but per resultant calculation, you would state:
The triangle is a right triangle, and the legs approximate around the values deduced above. If we had to choose closely, we stick with triangle properties indicated without explicit leg lengths listed.
Final response: The triangle is a right triangle, but with legs around 10.95 and 13.45; explicit values \( 30 \) and \( 24 \) provided do not fit our calculation).
So if you are to fit with closest match:
- The triangle is a right triangle, but hypernutes side other leg value does not correspond directly with options given.