If the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point) Responses The triangle is a right triangle, and the legs are 30 and 24. The triangle is a right triangle, and the legs are 30 and 24. The triangle is a right triangle with a missing leg length of 24. The triangle is a right triangle with a missing leg length of 24. The triangle is a right triangle with a missing side of 34.99. The triangle is a right triangle with a missing side of 34.99. The triangle is a right triangle, and the hypotenuse is 18.

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GPT-4o mini · Answer

To solve the equation $182 + b^2 = 302$: 1. Subtract 182 from both sides: $$ b^2 = 302 - 182 $$ $$ b^2 = 120 $$ 2. Take the square root of both sides to find $b$: $$ b = \sqrt{120} $$ $$ b = \sqrt{4 \times 30} = 2\sqrt{30} \approx 10.95 $$ Now, interpreting the context of the problem in relation to a triangle: Given that the equation $a^2 + b^2 = c^2$ (the Pythagorean theorem) can be inferred where $a$ and $b$ are the legs and $c$ is the hypotenuse, we can determine that: - If the legs of the triangle are $24$ and $30$, then the hypotenuse can be calculated as follows: $$ c^2 = 24^2 + 30^2 = 576 + 900 = 1476 $$ $$ c = \sqrt{1476} \approx 38.4 $$ However, from the original equation $182 + b^2 = 302$, if we refer back to $b^2 = 120$, this indicates that we have established a relationship between the legs (including one leg as $b$). Options interpreted: - The triangle is determined to be a right triangle. - Given the calculations, we might not conclude directly that $b$ corresponds exactly to $24$ but rather that $b$ represents an achievable leg length derived. However, since the calculated leg based on $b^2 = 120$ does not equate to $34.99$, nor does it indicate segments mentioned, the established conclusion is: **The triangle is a right triangle with a missing leg length of approximately 10.95 (or $b = \sqrt{120}$).** Please clarify if you intended certain numerical values so I can assist further on specific leg assignments.