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 legs are 30 and 24.
The triangle is a right triangle, and the hypotenuse is 18.
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 legs are 30 and 24.
The triangle is a right triangle, and the legs are 30 and 24.
To determine what we know about the triangle described by the equation 18^2 + b^2 = 30^2, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have the equation 18^2 + b^2 = 30^2. By simplifying, we get 324 + b^2 = 900. By subtracting 324 from both sides, we have b^2 = 576.
To find the value of b, we can take the square root of both sides of the equation. √b^2 = √576. The square root of 576 is 24. Therefore, b = 24.
So, from the equation, we know that the missing length of one of the legs of the triangle is 24 units. Therefore, the correct response is "The triangle is a right triangle with a missing leg length of 24."