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 hypotenuse is 18.
The triangle is a right triangle, and the hypotenuse is 18.
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, 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 with a missing leg length of 24.
The triangle is a right triangle, and the legs are 30 and 24.
ok
Great! So in this triangle, we know that one of the legs is 30 units long and the other leg is 24 units long.
To determine what we know about the triangle, we can analyze the equation 18^2 + b^2 = 30^2. This equation 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) equals the sum of the squares of the lengths of the other two sides (the legs).
In this case, the equation tells us that 18^2 + b^2 = 30^2. By calculating these values, we find that 18^2 equals 324 and 30^2 equals 900. Therefore, the equation becomes 324 + b^2 = 900.
To find the value of b, we can subtract 324 from both sides of the equation, resulting in b^2 = 900 - 324, or b^2 = 576. Taking the square root of both sides, we get b = √576, which simplifies to b = 24.
So, from the equation it is clear that the triangle is a right triangle, and the missing leg length (represented by b) is 24 units. Therefore, the correct answer is: "The triangle is a right triangle with a missing leg length of 24."