# Chapter 9: Theodolite Traversing¶

### ch-9 page 302 pb-1¶

In [1]:
from __future__ import division

import math

l1=75.5;
l2=180.5
l3=60.25

t1=30.4;t2=69.4;t3=30.5;
t2=180-t2;
t3=180-t3;

Lc1=l1*math.cos(t1*(math.pi/180))
Lc2=l2*math.cos(t2*(math.pi/180))
Lc3=l3*math.cos(t3*(math.pi/180))

Ls1=l1*math.sin(t1*(math.pi/180))
Ls2=l2*math.sin(t2*(math.pi/180))
Ls3=-l3*math.sin(t3*(math.pi/180))

print(Lc1,Lc2,Lc3);
print(Ls1,Ls2,Ls3);
Lc4=-Lc1-Lc2-Lc3;
Ls4=-Ls1-Ls2-Ls3;

print(Lc4,Ls4);

t4=-math.atan(Ls4/Lc4);
t4=t4*(180/math.pi);

l4=math.sqrt(Lc4*Lc4+Ls4*Ls4);

print('distance DA=',l4);
print('bearing of DA=',t4);

(65.11978202514794, -63.50741753704864, -51.91315691660193)
(38.20554919114786, 168.9587462008847, -30.579186368382416)
(50.300792428502625, -176.58510902365015)
('distance DA=', 183.60955979422673)
('bearing of DA=', 74.10023981818601)


### ch-9 page 304 pb-2¶

In [2]:
from __future__ import division

import math

l1=100;
l2=80;
l3=60;

t2=39.5;t3=40.5;t4=49.75;

L2=l2*math.cos(t2*(math.pi/180));
L3=l3*math.cos(t3*(math.pi/180));

D2=l2*math.sin(t2*(math.pi/180));
D3=l3*math.sin(t3*(math.pi/180));

l41=(157.86+math.sqrt(157.86*157.86-4*1757.5))/2;
l42=(157.86-math.sqrt(157.86*157.86-4*1757.5))/2;

print('length of DA is',l41,'or',l42);

print('when length of DA ,L=145.8')

k=math.cos(t4*(math.pi/180))
k1=(L2+L3-(k*l41))/100;
t1=math.acos(k1);
t1=t1*(180/(math.pi))
print('bearing at AB is=N',t1)

print('when length of DA ,L=12.04')

k=math.cos(t4*(math.pi/180))
k1=(L2+L3-(k*l42))/100;
k1=k1+0.004;
t11=math.acos(k1);
t11=t11*(180/(math.pi))
print(k1)
print('bearing at AB is=N',t11)

('length of DA is', 145.80634036039953, 'or', 12.053659639600497)
when length of DA ,L=145.8
('bearing at AB is=N', 82.44640641462031)
when length of DA ,L=12.04
0.999661660714
('bearing at AB is=N', 1.4904797844587976)


### ch-9 page 305 pb-3¶

In [3]:
#ch-9 page 305   pb-3
from __future__ import division

import math

l1=100.5;l3=75;l4=50.5;
t1=30.5;t2=45;t3=40.5;t4=60;t5=40.25;

L1=l1*math.cos(t1*(math.pi/180))
L3=-l3*math.cos(t3*(math.pi/180))
L4=-l4*math.cos(t4*(math.pi/180))

print('latitude of AB,CD,DE are',L1,L3,L4);
D1=l1*math.sin(t1*(math.pi/180))
D3=-l3*math.sin(t3*(math.pi/180))
D4=-l4*math.sin(t4*(math.pi/180))
print('Depature of AB,CD,DE are',D1,D3,D4);

L2_L5=-(L1+L3+L4);
D2_D5=-(D1+D3+D4);
print(L2_L5,D2_D5)

k=0.117;
l5=(L2_L5+D2_D5)/(k);

k1=0.763;

l2=(k1*l5)-L2_L5;
l2=l2/0.707;

print('length of BC=',l2);
print('length of EA=',l5);

('latitude of AB,CD,DE are', 86.59373062437335, -57.03044742000232, -25.250000000000007)
('Depature of AB,CD,DE are', 51.00760547755076, -48.708603624763775, -43.73428289111415)
(-4.313283204371025, 41.43528103832716)
('length of BC=', 348.51410778926174)
('length of EA=', 317.28203276885586)


### ch-9 page 307 pb-4¶

In [4]:
#ch-9 page 307   pb-4
from __future__ import division

import math

l1=75.5;l2=80.25;l3=75;
t1=30.25;t2=40.5;t3=60.5;

L1=l1*math.cos(t1*(math.pi/180))
L2=-l2*math.cos(t2*(math.pi/180))
L3=-l3*math.cos(t3*(math.pi/180))
print('latitudes of AQ,QR,RB are',L1,L2,L3);

D1=l1*math.sin(t1*(math.pi/180))
D2=l2*math.sin(t2*(math.pi/180))
D3=-l3*math.sin(t3*(math.pi/180))
print('Depature of AQ,QR,RB are',D1,D2,D3);

L4=-(L1+L2+L3);
D4=-(D1+D2+D3);

l4=math.sqrt(L4*L4+(D4*D4));

print('length of AB=',l4,'meters');

('latitudes of AQ,QR,RB are', 65.21958064293187, -61.02257873940248, -36.93176700776003)
('Depature of AQ,QR,RB are', 38.03493526693723, 52.118205878497236, -65.27667719549248)
('length of AB=', 41.114514530539196, 'meters')


### ch-9 page 308 pb-5¶

In [5]:
#ch-9 page 308   pb-5
from __future__ import division

import math

l1=150.5;l2=200;l3=125;
t1=50.25;t2=30.5;t3=60.5;

L1=-l1*math.cos(t1*(math.pi/180))
L2=-l2*math.cos(t2*(math.pi/180))
L3=-l3*math.cos(t3*(math.pi/180))
print('latitudes of BQ,QP,PA are',L1,L2,L3);

D1=l1*math.sin(t1*(math.pi/180))
D2=-l2*math.sin(t2*(math.pi/180))
D3=-l3*math.sin(t3*(math.pi/180))
print('Depature of BQ,QP,PA are',D1,D2,D3);

L4=-(L1+L2+L3);
D4=-(D1+D2+D3);

l4=math.sqrt(L4*L4+(D4*D4));

print('length of AB=',l4,'meters');

t4=math.atan(D4/L4);
t4=t4*(180/math.pi);
print('bearing of AB=',t4);

PAB=t3-t4;
QBA=t1+t4;

print('PAB=',PAB,'QBA=',QBA);

('latitudes of BQ,QP,PA are', -96.23556979807799, -172.32583208830516, -61.552945012933385)
('Depature of BQ,QP,PA are', 115.71069572705566, -101.50767259214082, -108.79446199248746)
('length of AB=', 343.3992171422471, 'meters')
('bearing of AB=', 15.989201746570728)
('PAB=', 44.51079825342927, 'QBA=', 66.23920174657073)


### ch-9 page 308 pb-6¶

In [6]:
#ch-9 page 308   pb-6
from __future__ import division

import math

l1=130;l2=215;l3=155.5;l4=120;
t1=20.5;t2=60.25;t3=30.5;t4=80.5;

L1=l1*math.cos(t1*(math.pi/180))
L2=l2*math.cos(t2*(math.pi/180))
L3=-l3*math.cos(t3*(math.pi/180))
L4=l4*math.cos(t4*(math.pi/180))
print('latitudes of AB,BC,CD,DE are',L1,L2,L3,L4);

D1=l1*math.sin(t1*(math.pi/180))
D2=l2*math.sin(t2*(math.pi/180))
D3=l3*math.sin(t3*(math.pi/180))
D4=l4*math.sin(t4*(math.pi/180))
print('Depature of AB,BC,CD,DE are',D1,D2,D3,D4);

L5=-(L1+L2+L3+L4);
D5=-(D1+D2+D3+D4);

l5=math.sqrt(L5*L5+(D5*D5));

print('length of EA=',l5,'meters');

t5=math.atan(D5/L5);
t5=t5*(180/math.pi);
print('bearing of EA=',t5);

FA=l5/2;
l6=FA;
t6=t5;
L6=-l6*math.cos(t6*(math.pi/180))
D6=-l6*math.sin(t6*(math.pi/180))

L7=-(L1+L2+L6)
D7=-(D1+D2+D6)

t7=math.atan(D7/L7);
t7=t7*(180/math.pi);
print('bearing from F to C is =',t7);

l7=math.sqrt(L7*L7+(D7*D7));

print('distance from F to C is =',l7);

('latitudes of AB,BC,CD,DE are', 121.76738460229168, 106.68654829016975, -133.98333444865727, 19.805712703281312)
('Depature of AB,BC,CD,DE are', 45.52695956373076, 186.6627451151656, 78.9222154403895, 118.35427218446777)
('length of EA=', 444.4100422146986, 'meters')
('bearing of EA=', 75.09947760257306)
('bearing from F to C is =', 5.818201574554788)
('distance from F to C is =', 172.2028708809785)


### ch-9 page 308 pb-7¶

In [7]:
#ch-9 page 308   pb-7
from __future__ import division

import math

l1=725;l2=1050;l3=1250;l4=950;l5=575;
t1=60;t4=55.5;t5=2.75;

L1=l1*math.cos(t1*(math.pi/180))
L4=-l4*math.cos(t4*(math.pi/180))
L5=-l5*math.cos(t5*(math.pi/180))
print('latitudes of AB,DE,EA are',L1,L4,L5);

D1=l1*math.sin(t1*(math.pi/180))
D4=-l4*math.sin(t4*(math.pi/180))
D5=-l5*math.sin(t5*(math.pi/180))
print('Depature of AB,DE,EA are',D1,D4,D5);

t2_t3=math.acos(0.1750);
t2_t3=180-(t2_t3*(180/math.pi));

print('t2-t3=',t2_t3);

t3=math.asin(0.6035);
t3=t3*(180/math.pi);
t2=t2_t3-t3;
t2=math.ceil(t2);

print('Bearing of BC is',t2);
print('Bearing of CD is',t3);

('latitudes of AB,DE,EA are', 362.50000000000006, -538.0859250785912, -574.3378222288467)
('Depature of AB,DE,EA are', 627.8684177437179, -782.9198791909149, -27.587423899772766)
('t2-t3=', 100.07865810778766)
('Bearing of BC is', 63.0)
('Bearing of CD is', 37.12098009569709)