Question

Triunghiul dreptunghic ABC m(A)=90° are cateta AB=12 si m (B)= 60° . Calculati AC BC si inaltimea AD. Urgent va roog

Answer 1

inΔABC m(∡A)=90° si m(∡B)=60°⇒m(∡C)=30°⇒conform th. ∡30°
AB=BC/2⇒BC=AB×2=12×2⇒BC=24cm
in ΔABC aplic th.pit.⇒AC²=BC²-AB²=24²-12²=576-144=432⇒AC=√432⇒
⇒AC=12√3cm
conform th. inaltimii⇒AD×BC=AC×AB⇒AD×24=12√3×12⇒AD=6√3cm

Answer 2

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