If the equation 18^2 + b^2 = 30^2

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 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 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.

Answer 1

To analyze the equation \( 18^2 + b^2 = 30^2 \), we can use the properties of right triangles as described by the Pythagorean theorem.

First, we can rewrite the equation:

\[ 18^2 + b^2 = 30^2 \]

Calculating \( 30^2 \):

\[ 30^2 = 900 \]

Calculating \( 18^2 \):

\[ 18^2 = 324 \]

Now we substitute these values into the equation:

\[ 324 + b^2 = 900 \]

Next, subtract 324 from both sides:

\[ b^2 = 900 - 324 \] \[ b^2 = 576 \]

Now take the square root of both sides to find \( b \):

\[ b = \sqrt{576} = 24 \]

This means that one leg of the triangle is 18, the other leg is 24, and the hypotenuse is 30.

Therefore, the correct response regarding the properties of the triangle is:

The triangle is a right triangle with a missing leg length of 24.