Question

in triunghiul ABC , masura unghiului A= 105 grade, masura unghiului B= 30 grade,iar inaltimea din A are lungimea AD=20 cm.Calculati aria triunghiului.

HELP VA ROOOOG!!

Answer 1

<C=180-105-30=45
In ΔADC: D=90
ctg45=CD/AD
1=CD/20         CD=20
In ΔADB:D=90
ctg30=DB/AD
√3=DB/20        DB=20√3

BC=CD+DB=20+20√3
Aria=BCxAD/2=(20+20√3)x20/2=20x20(1+√3)/2=200(1+√3)cm²

Answer 2

AD=20 cm
m(<CAD)=m(<ACD)=45⁰ ⇒ AD=DC=20 cm
in triunghiul ABD
tg 30⁰=AD/BD
1/√3=20/BD
BD=20√3 cm
BC=20+20√3=20(1+√3) cm
A=20(1+√3)x20/2=200(1+√3) cm²