Question

Fie Triunghiul ABC in care BC=8 cm AB=6 radical din 3 cm si măsura unghiului ABC = 60°.Aflati aria triunghiului

Answer 1

fie AP⊥BC=>AP->inaltime

In ΔAPB , m(∡P)=90°=>sinB=AP/AB=>AP=ABsinB=6√3*√3/2=3*3=9 cm

A=BC*AP/2=8*9/2=4*9=36 cm²

Answer 2

Explicație pas cu pas:

BD⊥AC

BD-inaltime

m(<ABD)=30°

m(<DBC)=30°

sin 30°=AD/AB

1/2=AD/6√3

AD=6√3/2

AD=3√3(cm);

sin 30°=DC/BC

1/2=DC/BC

1/2=DC/8

DC=4(cm);

cos 30°=BD/AB

√3/2=BD/6√3

2BD=18

BD=9(cm);

AC=AD+DC=(3√3+4)cm.

A=AC*BD/2

A=[(3√3+4)*9]/2

A=(27√3+36)/2

A=9(3√3+4)/2

A=4,5(3√3+4)

A=(13,5√3+18)cm².

Bafta!