Answer:
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
we know that
In the right triangle XYZ
[tex]cos(Y)=\frac{ZY}{XY}[/tex] ---> adjacent side divided by the hypotenuse
substitute the values
[tex]cos(30\°)=\frac{ZY}{4}[/tex]
Remember that
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
so
substitute
[tex]\frac{\sqrt{3}}{2}=\frac{ZY}{4}[/tex]
[tex]ZY=(4)\frac{\sqrt{3}}{2}[/tex]
[tex]ZY=2\sqrt{3}\ units[/tex]
step 2
[tex]sin(Y)=\frac{XZ}{XY}[/tex] --> opposite side divided by the hypotenuse
substitute the values
[tex]sin(30\°)=\frac{XZ}{4}[/tex]
Remember that
[tex]sin(30\°)=\frac{1}{2}[/tex]
so
[tex]\frac{1}{2}=\frac{XZ}{4}[/tex]
[tex]XZ=2\ units[/tex]
step 3
[tex]tan(Y)=\frac{XZ}{ZY}[/tex] --> opposite side divided by adjacent side
substitute the values
[tex]tan(Y)=\frac{2}{2\sqrt{3}}[/tex]
[tex]tan(Y)=\frac{1}{\sqrt{3}}[/tex]
Simplify
[tex]tan(Y)=\frac{\sqrt{3}}{3}[/tex]
so
StartFraction StartRoot 3 EndRoot Over 3 EndFraction
