If the equation 182 + b2 = 302 is found to be true, what do we know about the triangle?(1 point)
Responses
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 hypotenuse is 18.
The triangle is a right triangle, and the hypotenuse is 18.
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 provided equation is of the form:
\[a^2 + b^2 = c^2\]
Which is the Pythagorean theorem. This theorem applies to right triangles and states that the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c).
In the equation given:
\[18^2 + b^2 = 30^2\]
We are given that \(a = 18\) and \(c = 30\), and we need to find \(b\). Let's solve for \(b\):
\[324 + b^2 = 900\]
\[b^2 = 900 - 324\]
\[b^2 = 576\]
\[b = \sqrt{576}\]
\[b = 24\]
Thus, we know the following information about the triangle:
- The triangle is a right triangle since the Pythagorean theorem holds.
- One leg of the triangle is 18.
- The other leg of the triangle, which we just calculated, is 24.
- The hypotenuse of the triangle is 30.
Therefore, the correct response from the provided options would be:
The triangle is a right triangle, and the legs are 30 and 24.