If the equation 18^2 + b^2 = 30^2 is found to be true, what do we know about the triangle?(1 point)
We know that the triangle is a right triangle.
We can infer that the given equation represents the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
In this case, the equation 18^2 + b^2 = 30^2 implies that the triangle is a right triangle, where one side measures 18 units, another side measures b units, and the hypotenuse measures 30 units.
To understand what we know about the triangle, let's analyze the equation 18^2 + b^2 = 30^2:
First, we need to recognize that this equation represents 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 other two sides.
In this case, the equation 18^2 + b^2 = 30^2 represents a right triangle where one of the legs has a length of 18 units, the other leg is of unknown length (represented by b), and the hypotenuse has a length of 30 units.
By solving this equation, we can find the value of b. Let's do that:
18^2 + b^2 = 30^2
324 + b^2 = 900
b^2 = 900 - 324
b^2 = 576
Taking the square root of both sides, we find:
b = ±√576
b = ±24
Therefore, we now know that the length of the second leg of the triangle (b) can be either 24 or -24 units.
In summary, if the equation 18^2 + b^2 = 30^2 is found to be true, we know that the triangle is a right triangle with one leg measuring 18 units, the hypotenuse measuring 30 units, and the other leg measuring either 24 or -24 units.