We are asked to solve for the height of the triangle such that the AB measurement is 12 units and the CB measurement is 10 units. We will assume that the given triangle is a right triangle so that we can apply hypotenuse theorem c² = b² + a² where c = AB (the hypotenuse), where CB = b and AC is still unknown.
AB² = CB² + AC²
12² = 10² + AC²
AC² = 12² - 10²
AC = 6.63
Therefore the height is 10 units and the base is 6.63 units and the hypotenuse is 12 units.