To analyze the given equation \(182 + b^2 = 302\), we can solve for \(b^2\):
\[ b^2 = 302 - 182 \] \[ b^2 = 120 \]
Next, we take the square root of both sides to find \(b\):
\[ b = \sqrt{120} \] \[ b = \sqrt{4 \times 30} = 2\sqrt{30} \]
The calculated value of \(b\) is approximately \(10.95\).
This suggests that we have a right triangle, where for a right triangle with legs 24 and \(b\) (which is the unknown leg calculated), the hypotenuse can be calculated as follows:
- If one leg is 24 and the other leg is \(b\), then:
\[ (c, \text{ hypotenuse})^2 = (24)^2 + (b)^2 \] Where \(c^2\) would be equal to the sum of the squares of the two legs.
Neither of the options directly applies with the derived lengths, but since we know \(b\) fits into the calculation alongside 24, and relates to the triangle being a right triangle. However, confirming or denying the choices based on the actual leg and hypotenuse lengths is not perfectly fitting since the values provided in the options do not correspond perfectly with this derived side length.
Out of the choices provided:
- The triangle is a right triangle with a missing leg length of 24. (True since b=10.95 does not match up perfectly.)
Thus, the correct answer is:
The triangle is a right triangle with a missing leg length of 24.