Question

Triunghi dreptunghic ABC,m(unghi A)=90,are cateta AB=12 si m(unghi B)=60.Calculati lungimile segmentelor AC,BC si inaltimea AD​

Answer 1

AC=?

tg∧ B=60° = √3

tg B=cateta opusa/cateta alaturata⇒ tg B= AC/AB⇒√3=AC/12⇒AC=12√3 cm

In ΔABC , m(∧A)=90°=> Teorema lui Pitagora⇒ BC²=AC²+AB²⇒BC²=(12√3)² + 12⇒BC²=144×3 + 144⇒BC²=432+144⇒BC²=576⇒BC=√576⇒BC=24 cm

AD-inaltime inΔABC⇒teorema2 inaltimii⇒AD=AB×AC/BC⇒AD=12×12√3/24⇒(SIMPLIFICAM)⇒AC=6√3 cm