GANNETT.] 
SOLUTION OF TRIANGLES. 
15 
As all the angles and a side in each triangle are now known, the 
other sides, or the distances from P to the three given points, can be 
readily computed. 
PB 7194.87 I PB 
PA 8999. 89 ' 
PC 8107.98 
PA 8999. 89 
m 
7194.94 
PA 1388. 54 
PC ..-- 8107.91 
PA 1388. 54 
P B 5256. 29 
PA 2609. 75 
PC 6203. 63 
PA 2609.75 
The results are verified when both triangles give the same value for 
the line P A. 
GRAPHIC S0I.UTI0:N^ OF THE THREE-P0I:N^T PROBI.EM. 
1. When new point is within the triangle formed by the three 
points, point sought is within the triangle of error. 
2. When new point is on or near tlie circle passing through the 
other points, the location is iincertain. 
3. WHien new point is within either of the three shaded segments of 
the circle (see diagram below), orient on middle point; then the line 
from middle point lies between true point and point of intersection 
of lines from other two points. 
4. When new point is without the circle, orient on most distant 
point; then the point sought is always on the same side of the line 
from most distant point as the point of intersection of the other two 
lines. 
Note. — Since a location can be made from an}^ three points, whether 
correctly plotted or not, therefore alwa3\s check such locations by 
means of a fourth point if possible. 
Fig. 5.— Three-point problem; graphic sohition. 
