Question

What is the value of y?

Enter your answer, as an exact value, in the box.
y =

Answer 1

`y=2√(3)\ units`

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\°)=(BC)/(AB)`

`BC=ABcos(45\°)`

substitute the values

`BC=(2√(2))((√(2))/(2))=2\ units`

In the right triangle BCD

`tan(60\°)=(BD)/(BC)`

substitute the values

`√(3) =(y)/(2)\\ \\ y=2√(3)\ units`