Question

Ajutati-ma va rog !
Calculati aria triunghiului ABC daca :
a) AB=6 cm , AC= 10 cm si m(A)=30 grade
b) AB=5 , AC=8 , BC=7
c) AB=AC=BC=6
d) AB= 2radical2 , BC= 3radical2 si m(B)=90 grade
e) AB= 8radical6 , AC=BC , m(C)=90grade
f) AB= 2,4 cm ,AC=5cm si m(A)=150 grade

Answer 1

a) Se aplica formula a*b*sinC/2
A=6*10*1/2*1/2=15cm

b) se aplica formula lui Heron (https://ro.wikipedia.org/wiki/Formula_lui_Heron)

A=$\sqrt{10*5*2*3}$=$\sqrt{300}$=10$\sqrt{3}$

c) este un triunghi echilateral deci aria = $l^{2} \sqrt{3} /4$

A=9$\sqrt{3}$

d) Aria triungiului dreptunghic = C1*C2/2
A=2$\sqrt{2}$*3$\sqrt{2}$/2=6

e)
Notam AC=BC=l
Aplicand teorema lui Pitagora rezulta:
2$l^{2}$=384
l=8$\sqrt{3}$

Aplicam aceeasi formula ca si la punctul precedent:
A=8*8*3/2=96

f) A=AB*AC*sin150/2=12*1/2*1/2=3

sin(A+B)=sinA cosB+ sinB cosA
sin150=sin(90+60)=sin90*cos60+sin60*cos90=1/2