Answer:
[tex]h=\frac{\sqrt{3}}{2}b\ units[/tex]
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 equal to 60 degrees)
see the attached figure to better understand tyhe problem
Let
h ----> the height of an equilateral triangle
b ---> the length side of an equilateral triangle
In the right triangle ABD
Applying the Pythagorean Theorem
[tex]AB^2=AD^2+BD^2[/tex]
substitute the given values
[tex]b^2=(\frac{b}{2})^2+h^2[/tex]
[tex]b^2=\frac{b^2}{4}+h^2[/tex]
[tex]h^2=b^2-\frac{b^2}{4}[/tex]
[tex]h^2=\frac{3}{4}b^2[/tex]
square root both sides
[tex]h=\frac{\sqrt{3}}{2}b\ units[/tex]
