If the equation 18 ^ 2 + b ^ 2 = 30 ^ 2 is found to be true, what do we know about the triangle? (1 point)
O The triangle is a right triangle with a missing leg length of 24.
The triangle is a right triangle, and the hypotenuse is 18.
The triangle is a right triangle, and the legs are 30 and 24.
O The triangle is a right triangle with a missing side of 34.99.
The correct answer is:
The triangle is a right triangle, and the legs are 30 and 24.
To determine what we know about the triangle, we can analyze the equation given: 18 ^ 2 + b ^ 2 = 30 ^ 2.
Simplifying the equation: 324 + b ^ 2 = 900.
Subtracting 324 from both sides: b ^ 2 = 576.
Taking the square root of both sides: b = √576.
Calculating the square root: b = 24.
From the equation, we find that the missing leg length of the triangle is 24. Therefore, the correct answer is:
O The triangle is a right triangle with a missing leg length of 24.
To determine what we know about the triangle, we can analyze the given equation. The equation 18^2 + b^2 = 30^2 represents the Pythagorean theorem, which 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 (the legs).
By comparing the equation to the Pythagorean theorem, we can infer that the triangle is a right triangle. This means that one of the angles in the triangle measures 90 degrees.
However, the equation itself does not provide any specific information about the lengths of the legs or the hypotenuse. Therefore, we cannot determine the exact lengths of the legs or the hypotenuse of the triangle based solely on this equation.
Therefore, the correct answer is: The triangle is a right triangle, and we do not have enough information to determine the exact lengths of the legs or the hypotenuse.