Question

use the figure below to find the answer.
use special right triangles to solve for y.

Explanation:

Step1: Identify the triangle type

This is a \(45^{\circ}-45^{\circ}-90^{\circ}\) right - triangle. In a \(45^{\circ}-45^{\circ}-90^{\circ}\) triangle, the legs are equal (\(x = 7\)), and the hypotenuse \(y\) is related to the leg \(a\) by the formula \(y=a\sqrt{2}\).

Step2: Calculate the hypotenuse

Since \(a = 7\) (one of the legs), using the formula \(y=a\sqrt{2}\), we substitute \(a = 7\) into the formula. So \(y = 7\sqrt{2}\).

Answer:

\(y = 7\sqrt{2}\)