Question

using algebra find the value of each variable. write answers in simplest radical form. 12. right triangle with one leg 5, one acute angle 45°, legs x, y

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so legs are equal.

Step2: Solve for $x$

Legs are congruent, so $x = 5$.

Step3: Solve for hypotenuse $y$

Use 45-45-90 triangle rule: hypotenuse = leg $\times \sqrt{2}$
$y = 5\sqrt{2}$

Answer:

$x = 5$, $y = 5\sqrt{2}$