Explanation:
No figure has been provided so I'll assume an equilateral triangle as indicated in the figure below. Remember that this type of triangles are those whose sides have the same length. So some facts of ΔABC are:
1. Angles measure the same:
The angles measures the same as:
[tex]\angle A = \angle B = \angle C = 60^{\circ}[/tex]
2. Sides measure the same:
All sides measure the same, so:
[tex]a=b=c=x[/tex]
3. The height measures:
By Pythagorean Theorem:
[tex]If: \\ \\ a=b=c=x \\ \\ \\ and: \\ \\ h:height \\ \\ \\ x^2=h^2+(x/2)^2 \\ \\ h^2=x^2-(x/2)^2 \\ \\ h=\sqrt{3/4x^2} \\ \\ \boxed{h=\frac{\sqrt{3}x}{2}}[/tex]
