46 
HINTS TO TRAVELLERS, 
PART II, 
PLANE TRIGONOMETRY, PRELIMINARY REMARKS, 
AND MAP PROJECTIONS. 
The following formulae are of frequent use in all surveying problems. 
In right-angled triangles, B being the right angle, if either A or C is 
known, the other is found by subtracting the known angle from 90°. For 
the rest we have: 
A 
Case. 
Given. 
Required. 
Solution. 
1 { 
Hyp. AC 
Angles .. 
Base CB.. 
Perp. A B 
C B = A C X cos C. 
A B = A C X sin C. 
2 & 
Base C B 
Angles .. 
Perp. A B 
Hyp. AC 
A B = C B X tan C. 
A C = C B X sec C. 
4 & 5 | 
Hyp. AC 
Perp. A B 
Angles 
Base B C 
sin C = A B -f- AC; cos A = A B — AC. 
BC=V(AC + AB) X (AC - AB). 
6 *| 
Perp. A B 
Base B C 
Angles .. 
Hyp. AC 
tan C — A B -f- B C ; cot A = AB — B C. 
AC= B C X sec C. 
D 
