Pierwszy wiersz

$\frac{k}{m}=\mathrm{tg}\alpha$  

$\frac{1}{m}=\mathrm{tg}{30}^{\circ }$  

$\frac{1}{m}=\frac{\sqrt{3}}{3}$  

$1\cdot 3=\sqrt{3}\cdot m\mid \cdot \sqrt{3}$  

$3\sqrt{3}=3m\mid :3$  

$\underline{m=\sqrt{3}}$   

 

$\frac{k}{l}=\sin \alpha$  

$\frac{1}{l}=\sin {30}^{\circ }$  

$\frac{1}{l}=\frac{1}{2}$  

$1\cdot 2=l\cdot 1$  

$\underline{l=2}$  

 

$\beta ={180}^{\circ }-{90}^{\circ }-{30}^{\circ }=\underline{{60}^{\circ }}$  

 

Drugi wiersz

$\alpha ={180}^{\circ }-{90}^{\circ }-{10}^{\circ }=\underline{{80}^{\circ }}$  

 

$\frac{k}{l}=\sin \alpha$  

 

$\frac{k}{100}=\sin {80}^{\circ }$  

$k=100\cdot \sin {80}^{\circ }$  

$\sin {80}^{\circ }=0,9848$  

$k=100\cdot 0,9848=\underline{98,48}$  

 

$\frac{m}{l}=\sin \beta$  

$\frac{m}{100}=\sin {10}^{\circ }$  

$m=100\cdot \sin {10}^{\circ }$   

$\sin {10}^{\circ }=0,1736$     

$m=100\cdot 0,1736=17,36$  

 

Trzeci wiersz

Skorzystajmy z twierdzenia Pitagorasa:

$k^2+m^2=l^2$  

${\left(\sqrt{2}\right)}^2+{\left(2\sqrt{2}\right)}^2=l^2$  

$2+8=l^2$  

$10=l^2$  

$l=\underline{\sqrt{10}}$   

 

$\frac{k}{l}=\sin \alpha$  

$\frac{\sqrt{2}}{\sqrt{10}}=\sin \alpha$  

$\sqrt{\frac{2}{10}}=\sin \alpha$  

$\sin \alpha \approx 0,4472$  

Z tablic możemy odczytać, że:

$\sin {26}^{\circ }=0,4384$  

$\sin {27}^{\circ }=0,4540$  

Sprawdzamy, która wartość jest bliższa obliczonej:

$0,4472-0,4384=0,0088$  

$0,4540-0,4472=0,0068$  

A więc: 

$\alpha \approx \underline{{27}^{\circ }}$   

 

$\beta ={180}^{\circ }-{90}^{\circ }-{27}^{\circ }=\underline{{63}^{\circ }}$                

 

Czwarty wiersz

Stosujemy twierdzenie Pitagorasa:

${\left(\sqrt{3}\right)}^2+m^2={\left(2\sqrt{3}\right)}^2$  

$3+m^2=12$  

$m^2=9$  

$\underline{m=3}$   

 

$\frac{k}{l}=\sin \alpha$  

$\frac{\sqrt{3}}{2\sqrt{3}}=\sin \alpha$  

$\sin \alpha =\frac{1}{2}$  

$\underline{\alpha ={30}^{\circ }}$  

 

$\beta ={180}^{\circ }-{90}^{\circ }-{30}^{\circ }=\underline{{60}^{\circ }}$        

 

 

Uzupełnijmy tabelkę:

k	m	l	$\alpha$	$\eta$
1	$\sqrt{3}$	2	${30}^{\circ }$	${60}^{\circ }$
94,98	17,36	100	${80}^{\circ }$	${10}^{\circ }$
$\sqrt{2}$	$2\sqrt{2}$	$\sqrt{10}$	${27}^{\circ }$	${63}^{\circ }$
$\sqrt{3}$	$3$	$2\sqrt{3}$	${30}^{\circ }$	${60}^{\circ }$