Question

Raportul lungimilor catetelor e 5/12 ipotenuza e 26 calculations catetele si inaltimea tringhiului .Triunghi dreptunghic

Answer 1

[tex]\text{Notam catetele cu b si c,ipotenuza cu a si inaltimea cu h:}\\ \frac{b}{c}=\frac{5}{12}\Rightarrow\frac{b}{5}=\frac{c}{12}=k\Rightarrow b=5k,c=12k\\ \text{Aplicam teorema lui Pitagora:}\\ b^2+c^2=a^2\\ 25k^2+144k^2=676\\ 169k^2=676\\ k^2=4\Rightarrow \boxed{k=2}\\ b=5k\Rightarrow \boxed{b=10}\\ c=12k\Rightarrow \boxed{c=24}\\ \text{Pentru a afla inaltimea vom aplica formula:}\\ h=\frac{b\cdot c}{a}\\ \\ h=\frac{10\cdot 24}{26}\Rightarrow \boxed{h=\frac{120}{13}}[/tex]