The side length of an equilateral triangle is 20cm. How do you find the length of the altitude of the triangle?

Question

26642 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-09T12:41:13

I tried this:

Consider the diagram:
enter image source here
we can use Pythgoras theorem applied to the blue triangle giving:

#h^2+10^2=20^2#

rearranging:

#h=sqrt(20^2-10^2)=sqrt(300)=17.3cm#

Answer 2 · 2018-07-09T13:51:51

#17.3cm#

You can use trigonometry to find the altitude (same as height) of the triangle.

In an equilateral triangle, all the sides are equal and all the angles are equal to #60°#

The altitude is the side opposite the #60°# angle

#o/20 = sin 60°#

#o = 20 xx sin60°#

#o = 17.3cm#