FIND THE LENGTH OF THE ALTITUDE OF AN EQUILATERAL TRIANGLE IF THE MEASURE OF EACH SIDE IS 13cm.

This problem can be solved in two ways.

You can choose to use :
Phytagorean Theorem or
30°-60°-90° Right Triangle Theorem

Using Phytagorean Theorem

It states that the square of the hypotenuse is equal to the sum of the square of the other two side.
In symbol:

Note that this is only applicable to right triangle .

where:
a -length of the shorter leg
b -length of the longer leg
c -length of the hypotenuse

Solution:

Now let's compare the answer by using
30°-60°-90° Right Triangle Theorem

It states that the hypotenuse is equal to twice the length of the shorter leg, which is the side opposite to 30° angle.

In symbol:
a = c/2
b =a
c = 2a

Now let us go back to the problem and solve for the length of the altitude.

These formulas are applicable only to a 30°-60°-90° right triangle

Let triangle ABC be the equilateral triangle.
Solution:

Presenting the two ways it's now up to you which of the two you are comfortable to use with. Rest assured it will both lead you to the correct answer.

Assessment:
Let us find out how far you have learn.

Try to solve this using either of the two method. Just do what you are good at.

Problem:
The perimeter of a rhombus is 32cm. If one of its angles measures 120°. Find the lengths of the diagonals.

Have a nice day steemian!