To determine the properties of the triangle described by the equation \( 18^2 + b^2 = 30^2 \), we can analyze the equation itself.
This equation resembles the Pythagorean theorem, which states that for a right triangle, the sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse. In this case:
- The hypotenuse is 30.
- One leg is 18.
- The other leg is \( b \).
We can find \( b \) using the equation:
\[ b^2 = 30^2 - 18^2 \]
Calculating this gives:
\[ b^2 = 900 - 324 = 576 \]
Taking the square root of both sides gives:
\[ b = \sqrt{576} = 24 \]
Thus, we have confirmed that the triangle is a right triangle, the legs are \( 18 \) and \( 24 \), and the hypotenuse is \( 30 \).
From the options provided, the correct response is:
The triangle is a right triangle with a missing leg length of 24.