Question

In triunghiul dreptunghic ABC,cu m(A)=90°,AB=24 cm.Daca tg B=0,75,calculati aria si perimetrup triunghiului.

Answer 1

$tgB=\dfrac{AC}{AB}\Rightarrow \dfrac34=\dfrac{AC}{24}\Rightarrow AC=\dfrac{24\cdot3}{4}=18\ cm$

Cu teorema lui Pitagora avem:

$BC^2=AB^2+AC^2=24^2+18^2=576+324=900\Rightarrow$

$\Rightarrow BC=30\ cm.$

$A_{ABC}=\dfrac{18\cdot24}{2}=216\ cm^2.\ \ P_{ABC}=18+24+30=...$