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

Question

(1 point)

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.

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

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

Answer 1

To solve the equation \( 18² + b² = 30² \):

1. Calculate \( 18² \) and \( 30² \):

   • \( 18² = 324 \)
   • \( 30² = 900 \)

2. Substitute these values into the equation: \[ 324 + b² = 900 \]

3. Solve for \( b² \): \[ b² = 900 - 324 = 576 \]

4. Take the square root to find \( b \): \[ b = \sqrt{576} = 24 \]

Thus, we find that one leg (\( b \)) of the triangle is 24. Since we established \( 18 \) and \( 24 \) as the legs, and \( 30 \) as the hypotenuse, we can conclude:

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