Answer:
The length of the altitude of the triangle is [tex]4\sqrt{3}\ units[/tex]
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal interior angles that measures 60 degrees each
The altitude of the equilateral triangle is equal to the side NO
see the attached figure
In the right triangle LNO
Applying the Pythagoras Theorem
[tex]LN^2=LO^2+NO^2[/tex]
[tex]NO^2=LN^2-LO^2[/tex]
we have
[tex]LN=8\ units[/tex]
[tex]LO=8/2=4\ units[/tex]
substitute
[tex]NO^2=8^2-4^2[/tex]
[tex]NO^2=48[/tex]
[tex]NO=\sqrt{48}\ units[/tex]
simplify
[tex]NO=4\sqrt{3}\ units[/tex]
therefore
The length of the altitude of the triangle is [tex]4\sqrt{3}\ units[/tex]
