To solve the equation \(182 + b^2 = 302\), we first isolate \(b^2\):
\[ b^2 = 302 - 182 \]
Calculating the right side:
\[ b^2 = 120 \]
Next, we take the square root of both sides to solve for \(b\):
\[ b = \sqrt{120} \]
Calculating the square root:
\[ b = \sqrt{4 \times 30} = 2\sqrt{30} \approx 10.95 \]
The triangle seems to relate to the Pythagorean theorem, where \(a^2 + b^2 = c^2\). Here we see \(a^2 = 182\) and \(c^2 = 302\).
The legs are approximated as follows:
- One leg (\(a\)) can be calculated:
\[ a = \sqrt{182} \approx 13.49 \]
Thus, we interpret this triangle as a right triangle with sides approximately \(13.49\) and \(10.95\) (where one leg \(b\) was missing), and a hypotenuse calculated as follows:
\[ c = \sqrt{302} \approx 17.35 \]
From the analysis based on the given equation \(182 + b^2 = 302\), it proves that the triangle is confirmed as a right triangle with a missing leg length related to \(b\).
Thus, the correct response is:
The triangle is a right triangle with a missing leg length of approximately 10.95 (not 24).
None of the provided multiple-choice answers match this conclusion exactly, but the interpretation related to the Pythagorean theorem indicates the relationships involved.
1 answer