How long the altitude of an equilateral triangle with side length 10cm

Equilateral triangles have 3 sides of the same length, so if you split it down the middle, you will end up with one side length of 10cm and another with 5cm. Pythagorus can be used to find the missing side length, because the line of symmetry creates a right angle.

a^2 + b^2 = c^2

5^2 + b^2 = 10^2 (substitute given values in, remember the longest side, or the side opposite the right angle is c)

25 + b^2 = 100 (simplify)

b^2 = 75

b = 8.6603

Check answer

5^2 + 8.6603^2 = 10^2

25 + 75 = 100