[tex]1) \\ \displaystyle Se~da: \\ \Delta ABC = dreptunghic ~in~A \\ AB=3\;cm \\ sin\,C= \frac{3}{5} \\ Rezolvare: \\
a) \\ sin\,C= \frac{AB}{BC} ~~~\Rightarrow ~~~BC = \frac{AB}{sin\,C}=\frac{3}{\frac{3}{5}}= 3\times \frac{5}{3} = \boxed{5\;cm}[/tex]
[tex]2) \\
Se ~da: \\
ABCD = dreptunghi \\ AD = 9\;cm ~~~~~(latimea) \\ AC = 15\;cm~~~~~(diagonala) \\
Se cere: \\
DC = lungimea \\ P_{ABCD} = perimetrul ~dreptunghiului \\ S_{ABCD} = aria dreptunghiului \\ [/tex]
[tex]Rezolvare: \\
a) \\ In ~\Delta ADC avem:~\ \textless \ D=90^o ;~AD~si~DC=catete;~AC=ipotenuza \\
DC= \sqrt{AC^2-AD^2}= \sqrt{15^2-9^2}=\sqrt{225-81}=\sqrt{144}=\boxed{12\;cm} \\
b) \\ P = 2AD+2DC=2\times 9 + 2\times 12 = 18 + 24 = 42\;cm \\
c) \\ S_{ABCD} = AD \times DC = 9 \times 12 = 108 \; cm^2[/tex]
