Answer:
[tex]XY = \frac{4\sqrt 3}{3}[/tex]
Step-by-step explanation:
The question is illustrated with the attached figure.
Required
Determine XY
To solve for XY, we make use of the tan function, which states that:
[tex]tan\theta = \frac{Opposite}{Hypotenuse}[/tex]
In this case:
[tex]tan\ 60= \frac{YZ}{XY}[/tex]
Substitute 4 for YZ
[tex]tan\ 60= \frac{4}{XY}[/tex]
Make XY the subject
[tex]XY= \frac{4}{tan\ 60}[/tex]
[tex]tan\ 60 =\sqrt 3[/tex]
So, the expression becomes:
[tex]XY = \frac{4}{\sqrt 3}[/tex]
Rationalize:
[tex]XY = \frac{4 * \sqrt 3}{\sqrt 3 * \sqrt 3}[/tex]
[tex]XY = \frac{4\sqrt 3}{3}[/tex]
