Question

In triunghiul dreptunghic ABC , m (Â)=90° , se duc inaltime AD ( D € (BC)) si mediana AM , M € (BC) . Stiind ca AM = 20 cm si m(DÂM) = 30° (AC mai mic ca AB) , calculati inaltimea AD si laturile triunghiului ABC
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Answer 1

MD=20cm/2=10cm     AD=√400-100=√300=10√3
m(BAM)=m(MBA)=(180grade-120grade)/2=60 grade/2=30grade
m(DAC)=(90-60)grade=30grade
10√3=√3/2 ·AC        <=>    AC=10√3 /  √3/2=20
CD²=20²-10√3²=400-300=100    <=>  CD=10cm
AM=BM=20cm  
BC=20cm+10cm+10cm=40cm
AB=√(40²-20²)=√1200=20√3
ΔBAM=isoscel , ΔMAC=echilateral
    R-s: AB=20√3cm, BC=40cm  si  AC=20cm       AD=10√3cm