Question

What is the value of y? Enter your answer, as an exact value, in the box. y =

Answer 1

Answer:

$y=2\sqrt{3}\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

$AC=BC$ -----> by a 45°-90°-45° triangle

so

$cos(45\°)=\frac{BC}{AB}$

$BC=ABcos(45\°)$

substitute the values

$BC=(2\sqrt{2})(\frac{\sqrt{2}}{2})=2\ units$

In the right triangle BCD

$tan(60\°)=\frac{BD}{BC}$

substitute the values

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