ANSWER
The length of the altitude is [tex]3\sqrt{3}[/tex] units
EXPLANATION
The altitude of a triangle is the vertical height of the triangle.
From the diagram the altitude is [tex]a[/tex]
Method 1: We can use Pythagoras theorem to find [tex]a[/tex]
[tex]6^2=a^2+3^2[/tex]
[tex]6^2-3^2=a^2[/tex]
[tex]36-9=a^2[/tex]
[tex]27=a^2[/tex]
We take the square root of both sides,
[tex]\sqrt{27}=a[/tex]
[tex]\sqrt{9\times3}=a[/tex]
[tex]\sqrt{9} \times \sqrt{3}=a[/tex]
[tex]3\sqrt{3}=a[/tex]
Method 2 Using Trigonometry
[tex]sin(60\degree)=\frac{a}{6}[/tex]
[tex]6sin(60\degree)=a[/tex]
[tex]a=6\times \frac{\sqrt{3}} {2}[/tex]
[tex]a=3\sqrt{3}[/tex]
