Answer:
Step-by-step explanation:
An equilateral triangle is one with all angles measuring 60 degrees. An altititude drawn from the vertex angle splits that vertex angle into 2 equal angles, each measuring 30 degrees. The altitude also splits the base of the triangle into 2 equal length parts, each measuring 1/2a. Now we have this equilateral triangle split into 2 30-60-90 triangles, the vertex angle measuring 30, the base angle measuring 60 and the angle made by the bisection of the base is the 90. The altitude of the equilateral triangle is the height of one of these 30-60-90 triangles. Using the Pythagorean triple for a 30-60-90 special right triangle, the side across from the 30 is 1/2a, the side across from the 60 then is 1/2a√3 (or [tex]\frac{a\sqrt{3} }{2}[/tex], and the hypotenuse is a√3. The altitude is the side across from the 60 degree angle, so the answer you are looking for in terms of a is:
[tex]\frac{a\sqrt{3} }{2}[/tex]
