Question

determine the length of the hypotenuse for the given 45 - 45 - 90 triangle:

Explanation:

Step1: Recall the properties of a 45 - 45 - 90 triangle

In a 45 - 45 - 90 triangle, if the length of each of the legs is \(a\), then the length of the hypotenuse \(c\) is given by the formula \(c = a\sqrt{2}\). Here, \(a = 3\).

Step2: Calculate the hypotenuse

Substitute \(a = 3\) into the formula \(c=a\sqrt{2}\). So, \(c = 3\sqrt{2}\).

Answer:

\(3\sqrt{2}\)