To solve the equation \(182 + b^2 = 302\), we first isolate \(b^2\):
\[ b^2 = 302 - 182 \] \[ b^2 = 120 \]
Next, we take the square root of both sides to find \(b\):
\[ b = \sqrt{120} \approx 10.95 \]
This indicates that one side (leg) of the triangle is approximately 10.95. However, there is one detail we need to clarify.
If we consider the triangle to be a right triangle where this equation is representing the lengths of the two legs and the hypotenuse, we assume one leg is 18 (from the information provided) and the hypotenuse is the missing side (which we need to clarify).
Given that the equation is set up like the Pythagorean theorem, we need to find what the other sides would be. Let's analyze the available answers:
- The triangle is a right triangle with a missing side of 34.99. (Not applicable)
- The triangle is a right triangle with a missing leg length of 24. (Check this)
- The triangle is a right triangle, and the legs are 30 and 24. (Not true based on calculations)
- The triangle is a right triangle, and the hypotenuse is 18. (Not applicable)
Based on the information, let's verify if any of the given options prove to be true.
Checking Option 2 (Leg length of 24)
We can check this by assuming one leg is 24, and if b = \( \sqrt{120}\):
If the sides of a right triangle are \(24\) and \(10.95\), and using the Pythagorean theorem we would have \(24^2 + 10.95^2 = c^2\), solving for \(c\):
\[ 24^2 = 576 \] \[ (10.95)^2 \approx 120 \] \[ 576 + 120 = 696 \]
Taking the square root for the hypotenuse, we have approximately \( \sqrt{696} \approx 26.4\).
None of the provided statements appear to be true based on the calculations conducted. However, the calculated length of \(b\) indicates that a leg length of around \(10.95\) corresponds to the rest of what an adequate triangle would look like. It seems no option directly relates to the computed value, leading me to determine the correct conclusion isn't among the available options.
In conclusion, we cannot definitively assert any of the provided options since the triangle being correct appears logically mishandled or misrepresented by the options given. The triangle represents Pythagorean setups but lacks correct labels among the statements.