Question

The sides of an equilateral triangle are 8 units long.what is the length of the altitude of the triangle?

Answer 1

Answer:

Equilateral triangle implies each angle is 60 degree.

And any median is the altitude.

So, NT perpendicular LM, where T is the midpoint of [ML];

We use the Pythagorean Theorem in right triangle NTL ( NT = h; NL = a;

LT = a / 2 );

h² = a² - (a/2)² = a² - a²/4 = 4a²/4 - a²/4 = 3a²/4 ;

It follows that

h = √(3a²/4) = a√3/2 ≈ 0,866*a;

But, a = 8;

h ≈ 0,866 * 8 ≈ 6,928;

Step-by-step explanation: