Question

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 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. The triangle is a right triangle, and the hypotenuse is 18. The triangle is a right triangle with a missing leg length of 24.

Answer 1

To analyze the equation $182+b^2=302$, we first rearrange it to solve for $b^2$:

$$b^2=302-182$$ $$b^2=120$$

Next, we take the square root of both sides to find $b$:

$$b=\sqrt{120}$$ $$b\approx 10.95$$

Given that the equation resembles the Pythagorean theorem $a^2+b^2=c^2$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of a right triangle, this implies that $182$ is the square of one leg (which is $\sqrt{182}\approx 13.5$) and $b^2$ corresponds to the other leg while $302$ is the square of the hypotenuse.

Since $182$ represents $\sqrt{182}$ which is close to $14$ and $b=\sqrt{120}$, we can summarize that this triangle is a right triangle.

Now, considering the options provided:

1. The triangle is a right triangle, and the legs are 30 and 24.
2. The triangle is a right triangle, and the legs are 30 and 24.
3. The triangle is a right triangle with a missing side of 34.99.
4. The triangle is a right triangle with a missing side of 34.99.
5. The triangle is a right triangle, and the hypotenuse is 18.
6. The triangle is a right triangle with a missing leg length of 24.

None of the options seem to correctly represent the triangle derived from the calculation. However, we can correctly state that:

• The triangle is a right triangle.
• We found that one leg is approximately $10.95$ and the other leg is approximately $13.5$.

Therefore, if we must select the best match from the available options, the closest related statement to the right triangle is "The triangle is a right triangle with a missing leg length of 24" interpreting "missing leg" broadly for the context.