EXAMPLES 69 



Working with the triangle PQR and calling the sides p, q, and r, 

 then p = 7, q = 9-110, and r = 6-164. 



9 + 

 = 11-137 



Area = A = Vll-137 x 4-137 x 2-027 x 4-978 



= 21-55 

 . 43-10 



9-110 x 6-164 

 = 0-7676 

 P = 50 8' 

 . 43-10 



'^ ~ 7 x 6-164 



= 0-9989 

 Q = 87 18' 



si R= 43 ' 10 



= 0-6759 

 R = 42 32' 



These are the angles between the lines. 



If h p , h q , and h r are the perpendiculars drawn from the points 

 P, Q, and R respectively, 



43-10 

 then h p = = 6-157 



*.-*" *T 



- 0088 



6-164 



The angles between the lines can also be found in the following 

 manner : 



+ r 2 - z 



cos P 



cos Q 



2qr 

 = 0-6410 

 P = 50 8' 



2 + r 2 - ? 2 



cos R = 



2pr 

 = 0-0463 

 Q - 87 20' 

 p* + q 2 - 



2pq 

 - 0-7370 

 R = 42 31' 



