If the equation 182 + b2 = 302

Question

is found to be true, what do we know about the triangle?(1 point)
Responses

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, 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 with a missing leg length of 24.

Answer 1

To solve the equation $182+b^2=302$, we first isolate $b^2$:

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

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

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

Since the problem describes a triangle, it suggests using the Pythagorean theorem, which states that for a right triangle with legs $a$ and $b$, and hypotenuse $c$:

$$a^2+b^2=c^2$$

From the information given, we can interpret $182$ as one leg squared ($a^2$), and $b^2$ as the other leg squared. We can determine the lengths of the sides involved. We need to recognize the value obtained is related to the sides of a right triangle.

Given our findings, let's analyze the provided responses with respect to our calculations:

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

From our calculation, we consider $182$ corresponding to one leg squared and $120$ to the other leg squared, implying $b$ is actually the leg opposite to it.

To find the total of the hypotenuse:

The legs we find, $\sqrt{182}$ which is approximately $13.5$.

Additionally, $\sqrt{120}\approx 10.95$.

By Pythagorean theorem:

The hypotenuse $c$ would be:

$$c=\sqrt{182+120}=\sqrt{302}\approx 17.35$$

None of the answer choices fit exactly based on the calculations and results we've found, so the triangle characteristics detailed do not match.

If we assume 18 is a rounded hypotenuse acceptable by approximate evaluation but since none of the specific options is accurate or tightly matched, please use that understanding to decide selections or clarify based on the mathematical results resonating fundamentals about right triangles.

In conclusion, from the options presented, even though none fits perfectly based on the calculations, it seems we are to suggest the triangle has certain relationships provided. None exactly apply, leading to potentially the correct but less accurate assumptions without fitting numeric precision or clarity directly stemming from what we've established in calculations above, or finding $\sqrt{302}$ approximating toward given leg evaluations discussed.