Question

If the equation 18 to the power of 2 + b to the power of 2 = 30 to the power of 2
is found to be true, what do we know about the triangle?(1 point)
Responses

A. The triangle is a right triangle, and the hypotenuse is 18.

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

C. The triangle is a right triangle, and the legs are 30 and 24.

D. The triangle is a right triangle with a missing side of 34.99.

Answer 1

We start with the equation given:

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

Calculating each side:

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

Now substituting back into the equation:

\[
324 + b^2 = 900
\]

We can isolate \(b^2\):

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

Taking the square root of both sides gives:

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

Now we can evaluate what we know about the triangle. The sides of the triangle can be identified as 18 and 24 for the legs, and 30 as the hypotenuse. Therefore, the triangle is a right triangle with legs of 18 and 24, and the hypotenuse is 30.

The correct response is:

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