Question

use the rules of special right triangles to solve for x and y.
10
45°
x
x =
y =

Explanation:

Step1: Identify Triangle Type

This is a 45 - 45 - 90 right triangle (one angle 45°, right angle 90°, so third angle is 45°). In a 45 - 45 - 90 triangle, the legs are equal, and the hypotenuse \(y\) is leg \(\times\sqrt{2}\). The leg opposite 45° (vertical leg) is 10, so the other leg \(x\) (horizontal leg) is also 10 (since legs are equal in 45 - 45 - 90 triangle).

Step2: Calculate Hypotenuse \(y\)

Using the formula for hypotenuse in 45 - 45 - 90 triangle: \(y=\text{leg}\times\sqrt{2}\). Here, leg = 10, so \(y = 10\sqrt{2}\).

Answer:

\(x = 10\), \(y = 10\sqrt{2}\)