Answer:
see the explanation
Step-by-step explanation:
we know that
An equilateral triangle has three equal sides and three equal interior angles.
The measure of each interior angle is 60 degree
see the attached figure to better understand the problem
Let
b ----> the length side of the triangle
In the right triangle ABD
[tex]sin(60^o)=\frac{BD}{AB}[/tex] ----> by SOH (opposite side divided by the hypotenuse)
substitute the given values
[tex]sin(60^o)=\frac{6}{b}[/tex]
solve for b
[tex]b=\frac{6}{sin(60^o)}[/tex]
Remember that
[tex]sin(60^o)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]b=\frac{6}{\frac{\sqrt{3}}{2}}[/tex]
[tex]b=\frac{12}{\sqrt{3}}\ cm[/tex]
simplify
[tex]b=4\sqrt{3}\ cm[/tex]
