The height of the triangle would be ##5sqrt15 cm or 19.36 cm##

An isosceles triangle has two congruent sides.

The height of an isosceles triangle is also the median and the perpendicular bisector of the triangle dividing the base in half and forming two congruent right triangles.

Therefore, we can use the to solve for the height of the triangle.

##a^2 + b^2 = c^2##

##5^2 + h^2 = 20^2##

##25 + h^2 = 400##

##h^2 = 375##

##h = sqrt375##

##h = 5sqrt15cm##

##h = 19.36cm##