Question

Triunghiul ABC are m(<A)=105° ,m(<B)=45° si AB=6√2. Aflati masura unghiului C ,lungimile laturilor AC,BC si aria triunghiului.

Answer 1

m(C)=180°-105°-45°=>m(C)=30°
Construim,inaltimea,AD_l_BC
In,tr.dr.ADB,avem
sin45°=AD/AB
√2/2=AD/6√2=>AD=6
Cu,t.Pit.
AB²=AD²+BD²
72=36+BD²=>BD²=36=>BD=6

In,celalalt,tr.dr.ADC,avem
sin30°=AD/AC
1/2=6/AC=>AC=12
Cu,t.Pit.
AD²+DC²=AC²
36+DC²=144=>DC²=108=>DC=6√3
=>BC=6(1+√3)

A=6(1+√3)x6/2=>A=18(1+√3)