Proving Theorems on Special Right Triangles

Question

The length of one side of an equilateral triangle is 5√12 meters. Find the length of the altitude of the triangle.

Answer 1

base = 5sqr12 = a side of an equilateral triangle with each angle = 60 degrees = pi/3

half the base = 2.5sqr12

consider the right triangle (half of the equilateral triangle) with angle 60 degrees, base 2.5sqr12 and altitude = the height of the equilateral triangle.

tan60 = h/2.5sqr12 where h= height or altitude of the triangle

h=2.5sqr12tan60 = 2.5sqr12sqr3 = 2.5sqr(12x3) = 2.5sqr36 = 2.5(6) = 15

the triangle's altitude = 15 meters