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


Răspuns :

[tex]tgB=\dfrac{AC}{AB}\Rightarrow \dfrac34=\dfrac{AC}{24}\Rightarrow AC=\dfrac{24\cdot3}{4}=18\ cm[/tex]

Cu teorema lui Pitagora avem:

[tex]BC^2=AB^2+AC^2=24^2+18^2=576+324=900\Rightarrow [/tex]

[tex]\Rightarrow BC=30\ cm.[/tex]

[tex]A_{ABC}=\dfrac{18\cdot24}{2}=216\ cm^2.\ \ P_{ABC}=18+24+30=...[/tex]