Question

1. x = ______ y = ____ 15. x = ____ y = ______

Explanation:

Step1: Analyze the 45 - 45 - 90 triangle properties

In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(y\) is related to the leg \(x\) by the formula \(y = x\sqrt{2}\).

For problem 12:

Step1: Find \(x\)

Since the triangle is 45 - 45 - 90 and one leg is 4, then \(x = 4\) (legs are equal in 45 - 45 - 90 triangle).

Step2: Find \(y\)

Using the formula \(y=x\sqrt{2}\), substitute \(x = 4\). So \(y=4\sqrt{2}\).

For problem 15:

Step1: Find \(x\) and \(y\)

Given hypotenuse \(y = 9\sqrt{2}\). Using the formula \(y=x\sqrt{2}\), solve for \(x\). Divide both sides by \(\sqrt{2}\): \(x=\frac{9\sqrt{2}}{\sqrt{2}}=9\). Since it's a 45 - 45 - 90 triangle, \(y = 9\) (the other leg is equal to \(x\)).

Answer:

For problem 12: \(x = 4\), \(y = 4\sqrt{2}\)
For problem 15: \(x = 9\), \(y = 9\)