If the equation 18^2 + b^2 = 30^2 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 determine the properties of the triangle from the equation \( 18^2 + b^2 = 30^2 \), let's analyze the equation.

We can rearrange the equation to find \( b \):

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

Calculating \( 30^2 \) and \( 18^2 \):

\[ 30^2 = 900 \] \[ 18^2 = 324 \]

Now substitute these values:

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

Taking the square root of both sides:

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

Now we know the sides of the triangle are 18, 24, and 30. According to the Pythagorean theorem, if the squared lengths of the two shorter sides add up to the squared length of the longest side, the triangle is a right triangle. Here:

\[ 18^2 + 24^2 = 30^2 \]

Since:

\[ 324 + 576 = 900, \] \[ 900 = 900, \]

This confirms the triangle is indeed a right triangle.

Based on these calculations, the correct response is:

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