Question

Calculati lungimea laturii AC a triunghiului ABC, stiind ca BC=8, A=pi/4 si C=7pi/12

Answer 1

∡B=π-π/4-7π/4=(12π-3π-7π)/12=2π/12=π/6. Aplicam teorema sinusurilor:
$\frac{AC}{sinB}= \frac{BC}{sinA},avem.AC= \frac{BCsinB}{sinA}= \frac{8sin30}{sin45}=8* \frac{1}{2}* \sqrt{2}=4 \sqrt{2}$