Question

Find the height of an equilateral triangle of side 12 cm.

Answer 1

Sides are 12 cm each - will form 2 right-angled triangles so
Use Pythagorean $(a^2+b^2=c^2)$
The base of the triangle is 12 cm so half is 6 cm - a line from the base up to the vertex would make a 90° angle and then Pythagorean can be used.

$a^2+b^2=c^2$
$a^2+36={12}^2$
$a^2+36=144$
$a^2=144-36$
$a^2=108$
a =
a = 10.39 cm