If the equation 18 ^ 2 + b ^ 2 = 30 ^ 2 is found to be true, what do we know about the triangle? (1 point) 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, and the legs are 30 and 24. The triangle is a right triangle with a missing side of 34.99.
it is a right triangle, of course, but the hypotenuse is 30, and the legs are 18 and 24.
I apologize for the mistake. You are correct. The triangle is a right triangle, and the hypotenuse is 30. The legs are 18 and 24.
To determine what we know about the triangle, let's analyze the given equation 18^2 + b^2 = 30^2.
The equation represents the Pythagorean Theorem, which relates the lengths of the sides of a right triangle. According to the theorem, the sum of the squares of the lengths of the two legs (a and b) equals the square of the length of the hypotenuse (c).
In our equation, we have 18^2 for one leg and b^2 for the other leg, which should be equal to 30^2, the square of the hypotenuse.
By simplifying the equation, we have:
324 + b^2 = 900
Now we can solve for b:
b^2 = 900 - 324
b^2 = 576
Taking the square root of both sides of the equation, we find:
b = ±√576
b = ±24
So, we know that one leg of the triangle has a length of 24.
Now, let's determine if the triangle is a right triangle. If the equation is true, then a^2 + b^2 = c^2 must hold, where a and b represent the lengths of the two legs, and c represents the length of the hypotenuse.
In our case, a = 18, b = 24, and c = 30.
Substituting these values into the equation, we have:
18^2 + 24^2 = 30^2
324 + 576 = 900
900 = 900
Since the equation holds true, we can conclude that the triangle is indeed a right triangle, and the legs have lengths of 18 and 24.
Therefore, the correct answer is: The triangle is a right triangle, and the legs are 18 and 24.