Question

Se considera un triunghi ABC dreptunghic in A. Daca tgB=3/4 si AC=9. Calculati perimetrul unghiului

Answer 1

tgB = AC / AB 
3 /4 = 9 / AB       ⇒ AB =4·9 /3 = 36 / 3 = 12 
ipotenuza BC² =AB² + AC² = 9² + 12² = 81 + 144 = 225 
BC = √225 = 15 
perim.= AB +BC + AC = 12 + 15 + 9 = 36

Answer 2

   
[tex]\displaystyle \\ AC=\boxed{9~cm} \\ \\ \text{tg} B = \frac{\text{cateta opusa}}{\text{cateta alaturata}} = \frac{AC}{AB} = \frac{9}{AB} = \frac{3}{4} \\ \\ \Longrightarrow~~ AB= \frac{4\times 9}{3} = 4\times 3=12 ~cm \\ \\ BC = \sqrt{AB^2 + AC^2}= \sqrt{12^2 + 9^2}= \sqrt{144 + 81}= \sqrt{225}= \boxed{15~cm} \\ \\ P AB+AC+BC= 12+ 9 + 15 = \boxed{\boxed{36 ~cm }}[/tex]