20 PRACTICAL MATHEMATICS 



Case II. This case gives rise to three distinct examples accord- 

 ing to the position the given angle occupies with respect to the 

 two given sides. This angle may be : 



(a) Contained by the two sides. 



(b) Opposite the smaller side. 



(c) Opposite the larger side. 



(a) Let the two sides be 31 and 22 and the included angle 62. 

 Take the longest side as the base. 





= sin 62 = 0-8829 

 22 



h = 0-8829 x 22 = 19-42 



= cos 62 = 0-4695 

 22 



x = 0-4695 x 22 = 10-33 

 CB= Vh 2 + (31 - x) z 



= Vl9'42 2 + 20-67 2 = 28-36 



Also tan B = l - = |^|| = 0-9393 B = 43 12' 



C = 180 - (A + B) C = 74 48' 



(b) Let the two sides be 9 and 8, and the angle opposite to the 

 smaller side be 56. 



To draw the triangle, let AD be a line of indefinite length, 



/\ 

 make AB = 9 and BAD = 56. With B as centre and radius 



equal to 8 draw an arc of a circle cutting AD in the points Cj 

 and C. The triangles ABC and ABCj satisfy the given 

 conditions. 



Since the triangle BCC X is isosceles, the perpendicular BE 

 bisects the base. 



