Question

In triunghiul ABC se construieste inaltimea AD perpendiculara pe BC. Stiind ca masura lui BAC=75 grade, masura lui ABC=45 grade si AD=12 cm , calculati
perimetrul triunghiului ABC.

Answer 1

Tr ADB dreptunghic si isoscel => AD=BD=12 => conf th PItagora AB²=BD²+AD²=144+144=288 => AB=12√2. Tr ADC - dreptunghic, ungh DAC=30 grade => conf th unghi de 30 grade AC=2CD. Aplicam th pitagora AC²=CD²+AD² => 4CD²=CD²+144 => 3CD²=144 => CD²=144/3=48 => CD=4√3 => AC=8√3 si BC=12+4√3. P=AB+BC+AC=12√2+12+4√3+8√=12(√2+1+√3)