Obliczanie kątów

$$\cos A = \frac{{159,42}^{2} + {92,63}^{2} - {184,36}^{2}}{2 \bullet 159,42 \bullet 92,63} = 0,00021817$$

$$A = 8959'15"$$

$$\cos D = \frac{{91,84}^{2} + {159,42}^{2} - {184,36}^{2}}{2 \bullet 91,84 \bullet 159,42} = 0,29322$$

$$D = 7256^{'}01"$$

$$\cos E = \frac{{91,84}^{2} + {132,59}^{2} - {184,36}^{2}}{2 \bullet 91,84 \bullet 132,59} = - 0,32741$$

$$E = 1096^{'}93"$$

$$\cos I = \frac{{132,59}^{2} + {92,63}^{2} - {158,95}^{2}}{2 \bullet 132,59 \bullet 92,63} = 0,03645$$

$$I = 8754^{'}98"$$

Wyrównywanie kątów

$$\measuredangle A + \measuredangle D + \measuredangle E + \measuredangle I = 35957^{'}9"$$

$$= 02^{'}26,1"$$

$$\frac{}{4} = 00^{'}36,53"$$

Wartości kątów po wyrównaniu

A=89^o59’51,53”

D=72^o57’33,54”

E=109^o7’18,46”

I=87^o55’16,51”

Obliczanie azymutów

n=13

$$\alpha_{1} = 89 + n \bullet 1^{'} + n \bullet 10" = 8915'10"$$

$$\alpha_{2} = 8915^{'}10 + 180 - 1097'18,46 = 1607^{'}51,54"$$

$$\alpha_{3} = 1607^{'}51,54 + 180 - 8755'16,51 = 25212'35"$$

$$\alpha_{4} = 25212^{'}35 + 180 - 8959'51,53 = 34212^{'}43,5"$$

Obliczanie przyrostów

|DE|

$$x = 91,84 \bullet \cos{8915'10" =}91,84 \bullet 0,01304 = 1,20$$

$$y = 91,84 \bullet \sin{8915^{'}10" = 91,84 \bullet 0,99992 = 91,84}$$

|EI|

$$x = 132,59 \bullet \cos{1607^{'}51,54" = 132,59 \bullet ( - 0,94047) = - 124,70}$$

$$y = 132,59 \bullet \sin{1607^{'}51,54" = 132,54 \bullet 0,33987 = 45,06}$$

|IA|

$$x = 92,63 \bullet \cos{25212'35" = 92,63 \bullet ( - 0,30553) = - 28,30}$$

$$y = 92,63 \bullet \sin{25212'35" = 92,63 \bullet ( - 0,95218) = - 88,20}$$

|AD|

$$x = 159,42 \bullet \cos{34212^{'}43,5" = 159,42 \bullet 0,95219 = 151,80}$$

$$y = 159,42 \bullet \sin{34212^{'}43,5" = 159,42( - 0,28882) = - 48,70}$$

fx = 1, 20 + (−124,70) + (−28,30) + 151, 80 = 0, 00

fy = 91, 84 + 45, 06 + (−88,20) + (−48,70) = 0, 00

Obliczanie współrzędnych

X_d = 25300 + 13 • 1m + 13 • 1cm = 25313, 13m

Y_d = 35400 + 131m + 13 • 1cm = 35413, 13m

X_e = 25313, 13 + 1, 20 = 25314, 2

Y_e = 35413, 13 + 91, 84 = 35504, 97

X_i = 25314, 2 − 124, 70 = 25189, 5

Y_i = 35504, 97 + 45, 06 = 35550, 03

X_a = 25189, 5 − 28, 30 = 25161, 2

Y_a = 35550, 03 − 88, 20 = 35461, 83