Zad. 1
[tex]a=2\sqrt3\\b=\sqrt{13}\\c=5\\\\sin\alpha=\frac{a}c=\frac{2\sqrt3}5\\cos\alpha=\frac{b}c=\frac{\sqrt{13}}5\\tg\alpha=\frac{a}b=\frac{2\sqrt3}{\sqrt{13}}=\frac{2\sqrt{39}}{13}\\ctg\alpha=\frac{b}a=\frac{\sqrt{13}}{2\sqrt3}=\frac{\sqrt{39}}6[/tex]
Zad. 2
[tex]c=9a\\sin\alpha=\frac{a}c=\frac{a}{9a}=\frac19\\cos\alpha=\frac{b}c=\frac{b}{9a}\\tg\alpha=\frac{a}b\\ctg\alpha=\frac{b}a[/tex]
Zad. 3
[tex]e=14cm\\f=48cm\\\\(\frac12e)^2+(\frac12f)^2=a^2\\(7cm)^2+(24cm)^2=a^2\\a^2=49cm^2+576cm^2\\a^2=625cm^2\\a=25cm\\\\sin\alpha=\frac{7}{25}=0.28\\\alpha=16\\\\sin\beta=\frac{24}{25}=0.96\\\beta=74[/tex]
Katy w rombie:
[tex]2\alpha=2*16=32st.\\2\beta=2*74=148st.[/tex]
Romb ma 2 katy o mierze okolo 32° i dwa katy o mierze okolo 148°
