Question

In triunghiul dreptunghic ABC ,m(A) =90 ,m(C)= 30 ,AD perpendicular pe BC. Stiind ca DC=18 ,calculati lungimile segmentelor : AD,AB,AC si BC

Answer 1

Aplici in Δ ADC dreptunghic in D => tg C =AD/CD , dar tg 30°= √3/3 => AD=6√3
Aplici in Δ ABC teorema inaltimii => AD² = CD*DB => 108=18*DB => DB = 6 => BC = 18+6=24.
Aplici in Δ ABC , sin C = AB/BC , sin 30°= 1/2 => AB=12
si dupa cos C = AC/BC , cos 30° = √3/2 => AC= 12√3