Find the height for an equilateral triangle with side length 13.

Answer 1

side of an equilateral triangle = 13, each angle =60 degrees = pi/3

half the base = 13/2 = 6.5

use the Pythagorean Theorem

c^2 =a^2+b^2,

a^2 =c^2-b^2, c=13, b=6.5 where a=altitude or height

contruct a right triangle with height = one side=a, 13=hypotenuse, 6.5=the shorter side

height squared = the difference of the hypotenuse squared minus the other side square:

c^2 -b^2 = a^2 = height squared

13^2 - 6.5^2 = 169-42.25 = 126.75

height =sqr126.75 = about 11.26

or use trigonometry

half the equilateral triangle is

a 30-60-90 right triangle,

split the equilateral triangle vertically down the middle and look at the right triangle created

height = 13sin60 = 13(sqr3)/2 = 6.5(1.732) = about 11.258

it definitely helps to draw at least a rough sketch or graph

Answer 2

13 * sin(60) = 13*sqrt(3)/2