Oblique Angle Triangles 



tan 



Fundamental Formulae 

 c= 180 - (a-; b) etc. 



sin a : sin b : : A : B 

 (a b) : tan % (a - b) :: A -f- B : A - B 



Curve Location Formulae 



R = Radius 



D = Degree of curvature 

 L = Length of curve 

 A = Central angle 



A = 50 -5- // ^ A = 5730 -r- D 

 L = 100 A -f- D 

 A = DL -5- 100 

 D = 100 L H- L 



T = Tangent distance 



C = Long Cord 



M = Middle Ordinate 



E = External distance 



T = R tan */* A = E cot \ 



C = 2 R sin ft A 



M=R vm % A 



E = R wj*: >2 A = T /' 





Random Correction 



n the length of one side and the offset, sin a may be found in 

 correcting the direction of the random line by dividing the otfsf 

 by the measured distance, H; but where the correction angle is small 

 and the lengths of thesides differ insensibly, the offset is equal to the 

 arc. To find the deflection angle to turn from the random line, the 

 Radian Rule may be applied as follows: 



Multiply 57.3 by the offset and divide the pioihu t by the 

 measured length of the random line. The result will be in derimaU 

 of degrees and will be a trifle large for, a : 360 :: A : 27rr. 



