Question

In triunghiul ABC masura unghiului A=105° , m∡B=30°,iar inaltimea din A are lungimea AD=20.Calculati aria Δ

Answer 1

A+B+C=180, 105+30+C=180., C=45
AD inaltime deci AD⊥BC, ΔADC Δdreptunghic, tg C=AD/DC, tg 45=20/DC, DC=20, 
ΔADB Δdreptunghic, tgB=AD/BD, tg 30=20/BD, BD=20√3
BC=DC+BD=20+20√3
A ABC=ADxBC/2=20(20+20√3)/2=10(20+20√3)=200(1+√3)