Question

find y. 4 in 45° 45° y write your answer in simplest radical form. inches

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the ratio of the sides is \(1:1:\sqrt{2}\), where the hypotenuse \(c\) is related to the legs \(a\) and \(b\) (here \(a = b=y\)) by the formula \(c=a\sqrt{2}\).

Step2: Solve for \(y\)

Given \(c = 4\) inches. Using the formula \(c=y\sqrt{2}\), we can solve for \(y\) by \(y=\frac{c}{\sqrt{2}}\). Rationalizing the denominator: \(y=\frac{4}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{4\sqrt{2}}{2}=2\sqrt{2}\).

Answer:

\(2\sqrt{2}\) inches