Question

In ▲ dreptunghic ABC masura unghiului A e 90 de grade , se duc inaltimea AD , D apartine (BC) si mediana AM , M apartine lui (BC) , stiind ca AM e 20 de cm si masura unghiului DAM e 30 de grade , AC e mai mare decat AB , calculati AD si laturile ABC

Answer 1

deci am mediana ⇒AM≡MC≡MB
AM=20⇒MC≡MB=20 ⇒BC=2AM⇒BC=2×20⇒BC=40
ΔMAD: AM=20 masura unghi MAD =30 grade⇒MD=AM/2⇒MD=20/2⇒MD=10
ACUM ΔMAD stim AM=20 masura unghi MAD=30 grade si MS=10 
tangenta de 30 grade=10/AD
√3/3=10/AD⇒AD×√3=3×10⇒AD=30√3
ACUM IN ΔABC
latura CD= CM+MD⇒CD=20+10⇒CD=30
latura BD=BC-CD⇒DB=40-30⇒BD=10
AD INALTIME SI AD=30√3
AC=√BC×CD⇒AC=√40×30⇒AC=√1200⇒AC=20√3
AB=√DB×BC⇒AB=√40×10⇒AB=√400⇒AB=20