Question

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 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 hypotenuse is 18.
the triangle is a right triangle with a missing side of 34.99.

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) of a right - triangle and \(a\) and \(b\) are the legs.

Step2: Solve for \(b\)

Given \(18^{2}+b^{2}=30^{2}\), we can solve for \(b\):

$$
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$$

Since the equation \(a^{2}+b^{2}=c^{2}\) holds (\(18^{2}+24^{2}=30^{2}\)), it is a right - triangle. Here \(18\) and \(b = 24\) are the legs and \(30\) is the hypotenuse.

Answer:

The triangle is a right triangle with a missing leg length of 24.