Un triunghi dreptunghic ABC cu AB =16 AC=12 Me(BC) BM=4 . Lungimea segmentului AM Va rog frumos

Răspuns :

Tr dr in A,AC=12, AB=16⇒(Pitagora)BC=20 fie AD⊥BC, D∈BC
⇒AD=12*16/20=48/5=9,6=96/10=48/5
⇒CD=√(CA²-AD²)=√(16²-9,6²)=12,8
MD=CD-CM=12,8-4=8,8=88/10=44/5

in tr.dr ADM, AM²=AD²+MD²
AM²=(48/5)²+(44/5)²=(4/5)²(12²+11²)=(4/5)²(121+144)=(4/5)² *265
AM= (4/5)*√265


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