Given:
The figure of a right angle triangle.
To find:
The value of y.
Solution:
If a right angle triangle,
[tex]\cos \theta=\dfrac{Adjacent}{Hypotenuse}[/tex]
In the given right triangle,
[tex]\cos (30^\circ)=\dfrac{4\sqrt{3}}{y}[/tex]
[tex]\dfrac{\sqrt{3}}{2}=\dfrac{4\sqrt{3}}{y}[/tex]
[tex]\sqrt{3}\times y=2\times 4\sqrt{3}[/tex]
[tex]\sqrt{3}\times y=8\sqrt{3}[/tex]
Isolate the y variable.
[tex]y=\dfrac{8\sqrt{3}}{\sqrt{3}}[/tex]
[tex]y=8[/tex]
Therefore, the value of y is 8.