$\text{a)}$  

Wiemy, że:

$\sin \alpha =\frac{3}{5}$  

$\frac{a}{c}=\frac{3}{5}$     

$a=\frac{3}{5}c$  

 

Zatem otrzymujemy:

$\frac{c^2-a^2}{c^2}=\frac{c^2-{\left(\frac{3}{5}c\right)}^2}{c^2}=\frac{c^2-\frac{9}{25}{c}^2}{c^2}=\frac{\frac{25}{25}{c}^2-\frac{9}{25}{c}^2}{c^2}=\frac{\frac{16}{25}{c}^2}{c^2}=\frac{16}{25}$  

---

$\text{b)}$  

Korzystając z tw. Pitagorasa mamy:

$a^2+b^2=c^2$  

${\left(\frac{3}{5}c\right)}^2+b^2=c^2$  

$\frac{9}{25}{c}^2+b^2=c^2$  

$b^2=\frac{16}{25}{c}^2$  

$b=\frac{4}{5}c$  

 

Zatem otrzymujemy:

$\frac{b}{c}=\frac{\frac{4}{5}c}{c}=\frac{4}{5}$  

---

$\text{c)}$  

$\frac{11c-5a}{5a+c}=\frac{11c-5\cdot \frac{3}{5}c}{5\cdot \frac{3}{5}c+c}=\frac{11c-3c}{3c+c}=\frac{8c}{4c}=2$