136 Mr WALLACE, ON GEOMETRICAL THEOREMS, AND FORMULAE, 



given as an application of the rules of Trigonometrical calculation 

 rather than as a distinct problem. But as it frequently occurs in Tri- 

 gonometrical surveys it may be convenient to have formulae for its 

 solution in accordance with those which resolve the others. 



PROBLEM. (Figs. 7, 8, 9). 



Let A, B, C, D be four points or stations in a plane; there are 

 given BC, the distance between two of them, and all the angles of 



Fig. 8. 

 A 



Fig. 9- 



the triangles ABC, DBC which have BC as a common base ; to find 

 AB, the distance between their vertices. 



Following the notation used in Art. 10. I shall express the lines by 

 single letters, putting 



BC=a, AC=b, AB = c; DC=p, DB = q, AD^x. 



By Trigonometry, in the triangles ACD, ABD, BDC; 



A A .A 



sin hx _p sin eg _ x sm ap _ q ^ 



A"-^' . A ~ a' . A -»• 



sin hp sm ex ^ sm aq " 



