Explanation:
well, BHC is a right-angled triangle with BH being the Hypotenuse, and BC and CH being the legs.
so, per Pythagoras we know
BH² = BC² + CH²
we know BC (27 cm).
we need to find CH.
CHD is another right-angled triangle with CH being the Hypotenuse, and CD and DH being the legs.
again, per Pythagoras we get
CH² = CD² + DH² = 54² + 32² = 2916 + 1024 = 3940
CH = sqrt(3940) = 62.76941931... cm
now we can solve the original equation for BH :
BH² = BC² + CH² = 27² + 3940 = 729 + 3940 = 4669
BH = sqrt(4669) = 68.33008122... cm ≈ 68.3 cm