Question

8.7 special right triangles review
1)
$\frac{3sqrt{2}}{2}$
$x$
$y$
$x=\square$
$y=\square\sqrt{\square}\frac{\square}{\square}$

Explanation:

Step1: Identify triangle type

This is a 45-45-90 right triangle, so legs are equal: $y = \frac{3\sqrt{2}}{2}$

Step2: Calculate hypotenuse $x$

In 45-45-90 triangles, hypotenuse = leg $\times \sqrt{2}$.
$$x = \frac{3\sqrt{2}}{2} \times \sqrt{2}$$
Simplify: $\sqrt{2} \times \sqrt{2} = 2$, so $x = \frac{3 \times 2}{2} = 3$

Answer:

$x = 3$
$y = \frac{3\sqrt{2}}{2}$