Question

In triunghiu dreptunghic MNP,m(M)=90°,m(N)=30°,iar ipotenuza NP=12 cm.Daca MQ perpendiculara pe NP,Q apartine (NP),calculati MQ si perimetrul triunghiului MNP

Answer 1

sin30°=1/2
m(N)=30°=> MP/PN=1/2=>MP/12=1/2=> MP=6(cm)
cos30°=√3/2
m(N)=30°=>MN/NP=√3/2=>MN/12=√3/2=>MN=6√3 (cm)
In ▲MNP
MQ perpendicular pe MP
MP perpendicular pe MN
conform teoremei Inaltimii=>MQ=(MN×MP)/12=(6√3×6)/12=3√3(cm)

P▲=MN+MP+PN=6+6√3+12=18+6√3=6(3+√3) (cm)