Geometry question/

Question

In the ΔABC, the altitude AN = 24 in, BN = 18 in, AC = 40 in. Find AB and BC.

Answer 1

for triangle ANC

AC^2 = AN^2 + NC^2

40^2 = 24^2 + NC^2

NC = SQUARE ROOT (1600 - 576) = 32 in

then BC = BN + NC = 18 + 32 = 50 in

 

for triangle ANB

AB^2 = AN^2 + NB^2
AB^2 = 24^2 + 18^2
AB = SQUARE ROOT (576 + 324) = 30 in

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