SOLUTION: Find the altitude of an equilateral triangle that has side lengths of 4y. Express your answer in simplest radical form. I am a homeschooling mom and don't remeber how to do this

Algebra ->  Triangles -> SOLUTION: Find the altitude of an equilateral triangle that has side lengths of 4y. Express your answer in simplest radical form. I am a homeschooling mom and don't remeber how to do this      Log On


   

Question 220233: Find the altitude of an equilateral triangle that has side lengths of 4y. Express your answer in simplest radical form.
I am a homeschooling mom and don't remeber how to do this. Our book doesnt help either.
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The interior angles of an equilateral triangle
are 60-60-60, which adds up to
180 degrees, as they should.
The altitude divides the triangle into two
30-60-90 triangles, with the altitude being
opposite the 60 degree angle.
Call the altitude h
In this right triangle, sin%2860%29+=+h%2F%284y%29,
and sin%2860%29+=+sqrt%283%29%2F2
h%2F%284y%29+=+sqrt%283%29%2F2
Solve for h
h+=+4y%2Asqrt%283%29%2F2
h+=+2y%2Asqrt%283%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

If you construct an altitude of an equilateral triangle, then the altitude forms a right angle with the base. That means that you have now formed two 30-60-90 triangles, i.e. right triangles where the hypotenuse is one side of the equilateral triangle and the short leg is exactly one-half the measure of the hypotenuse. Now having a hypotenuse of 4 and a short leg of 2, we can use Pythagoras to calculate the measure of the long leg which is the same as the altitude of the equilateral triangle:






In general, if the measure of the length of a side of an equilateral triangle is , then the measure of an altitude is:


John