If the equation 182 + b2 = 302

Question

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

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, and the hypotenuse is 18.

Answer 1

To solve the equation \( 18^2 + b^2 = 30^2 \), we can first evaluate the squared values:

1. Calculate \( 18^2 \): \[ 18^2 = 324 \]

2. Calculate \( 30^2 \): \[ 30^2 = 900 \]

Now, we can set up the equation with these values: \[ 324 + b^2 = 900 \]

Next, we solve for \( b^2 \): \[ b^2 = 900 - 324 \] \[ b^2 = 576 \]

Now, take the square root to find \( b \): \[ b = \sqrt{576} = 24 \]

Now we know that one leg of the triangle is 18, the other leg is 24, and the hypotenuse is 30.

Given this information, the correct answer from the provided options is: The triangle is a right triangle with a missing leg length of 24.