>•, l, IS p[ 
214 
SUA’ VE VÌA'G. 
If we let sin a — s, and cos a = c, we have 
L = sD + cL ± Vr - (.D■ + U) + (sD + cLf 
(6) 
H ere there are two values of l m which will satisfy the equa 
tion, and so there are two solutions to the problem. If the 
surveyor has no knowledge whatever of either the unknown 
length or bearing, the problem is indeterminate. If he has 
seen the tract he could usually tell which length or which 
resulting bearing was the correct one, when the problem would 
become determinate. When l m is found, substitute in one of 
equations (5) and find 0 n . Pay careful attention to the signs 
of the trigonometrical functions of all bearings. When the 
two unknown courses are nearly at right angles with each 
other the problem is impracticable. 
Case III.— When two bearings are unknown. 
Let /' and /" be the known lengths of the courses whose 
bearings are unknown. Then the equations become 
1' sin d m -f-1" sin 6 n 
1' cos 6 m -|- l" cos 6 n 
D- 
L. 
• • (7) 
Whence 
cos 0 n = 
KL± D VL 2 - K 2 + D 2 
D l + U 
. (8) 
Where 
K = 
- r -\-D' + r 
21" 
This case is also indeterminate unless one is able to tell 
which of the two sets of bearings is the correct one.* 
CASE IV.— When the lengths of two courses are unknown. 
* And if the unknown sides are parallel, the problem is indeterminate. 
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