Răspuns:
Explicație pas cu pas:
∡B=60°
AD= 6 cm (inaltime)
.....................................
P=?
.............................
Demonstratie :
sin∡B= AD/AB
sin 60°=6/AB
sin 60°=√3/2
√3/2=²⁾6/AB
√3=12AB
AB= 12/√3=12√3/3=4√3cm
-
tg ∡B= AC /AB
tg 60°=AC/4√3
tg60°=√3
√3=AC/4√3
AC= 4√3*√3
AC=4*3
AC= 12 cm
-
teorema lui Pitagora
BC²=AC²+AB²
BC²=12²+(4√3)²
BC²=144+16*3
BC²=144+48
BC²=192
BC=√192
BC=8√3
-
P= AB+AC+BC
P=4√3+12+8√3
P=12√3+12
P= 12*(√3+1) cm ( perimetrul)
