If the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point)

Question

Responses

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, 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.

Answer 1

To determine information about the triangle from the equation \( 182 + b^2 = 302 \), we can solve for \( b^2 \):

1. Subtract 182 from both sides: \[ b^2 = 302 - 182 \]

2. Calculate the right side: \[ b^2 = 120 \]

3. Take the square root to find \( b \): \[ b = \sqrt{120} = \sqrt{4 \times 30} = 2\sqrt{30} \approx 10.95 \]

Considering the context of the triangle, we know that if we label one leg \( a = 18 \) and the other leg \( b \approx 10.95 \), using the Pythagorean theorem for a right triangle we also have:

\[ c^2 = a^2 + b^2 = 182 + 120 = 302 \] where \( c = \sqrt{302} \approx 17.35 \).

Analyzing the provided options:

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

None of the options accurately represent the findings from the equation given.

If we focus on the known values derived, we can conclude that the triangle has legs approximately 18 and 10.95, with a hypotenuse approximately equal to \( \sqrt{302} \), which does not match any of the responses provided. Please check the options again for accuracy.