▁of ▁a ▁right ▁triangle ▁is ▁one ▁half ▁the ▁product ▁of ▁the ▁two ▁legs . ▁As ▁a ▁formula ▁the ▁area ▁T ▁is ▁ ▁where ▁a ▁and ▁b ▁are ▁the ▁legs ▁of ▁the ▁triangle . ▁ ▁If ▁the ▁inc irc le ▁is ▁tang ent ▁to ▁the ▁hyp oten use ▁AB ▁at ▁point ▁P , ▁then ▁den oting ▁the ▁semi - per imeter ▁ ▁as ▁s , ▁we ▁have ▁▁ ▁and ▁, ▁and ▁the ▁area ▁is ▁given ▁by ▁ ▁This ▁formula ▁only ▁applies ▁to ▁right ▁tri angles . ▁ ▁Alt itudes ▁ ▁If ▁an ▁alt itude ▁is ▁drawn ▁from ▁the ▁vertex ▁with ▁the ▁right ▁angle ▁to ▁the ▁hyp oten use ▁then ▁the ▁triangle ▁is ▁divided ▁into ▁two ▁smaller ▁tri angles ▁which ▁are ▁both ▁similar ▁to ▁the ▁original ▁and ▁therefore ▁similar ▁to ▁each ▁other . ▁From ▁this : ▁ ▁The ▁alt itude ▁to ▁the ▁hyp oten use ▁is ▁the ▁geometric ▁mean ▁( mean ▁proportional ) ▁of ▁the ▁two ▁segments ▁of ▁the ▁hyp oten use . ▁ ▁Each ▁leg ▁of ▁the ▁triangle ▁is ▁the ▁mean ▁proportional ▁of ▁the ▁hyp oten use ▁and ▁the ▁segment ▁of ▁the ▁hyp oten use ▁that ▁is ▁adjacent ▁to ▁the ▁leg . ▁In ▁equations , ▁ ▁( this ▁is ▁sometimes ▁known ▁as ▁the ▁right ▁triangle ▁alt itude ▁theorem ) ▁ ▁where ▁a , ▁b , ▁c , ▁d , ▁e , ▁f ▁are ▁as ▁shown ▁in ▁the ▁diagram . ▁Thus ▁ ▁Moreover , ▁the ▁alt itude ▁to ▁the ▁hyp oten use ▁is ▁related ▁to ▁the ▁legs ▁of ▁the ▁right ▁triangle ▁by ▁ ▁For ▁solutions