22 



PRACTICAL MATHEMATICS 



If BC< h the arc does not cut the line at all, and it is im- 

 possible to draw the triangle. 



Working the question in the above manner enables us to decide 

 upon the particular form the question takes, for as we begin by 

 finding the value of h, it is a simple matter to compare that value 

 with the length of the smaller side. 



(c) Let the two sides be 17 and 20 and the angle opposite to 

 the larger side be 38. /\ 



Make AB = 17 and BAD = 38. With B as centre and radius 

 equal to 20 draw an arc of a circle cutting AD in the points C x 



^\E/V 



FIG. 5. 



The triangle BAC X does not satisfy the given conditions, since 

 the angle BAC X is the supplement of 38. 



4 - sin 38 = 0-6157 

 17 



h = 0-6157 x 17 = 10-47 



^- = cos 38 = 0-7880 

 17 



x = 0-7880 x 17 = 13-40 _ 

 y = V20 2 - h 2 = \/20 2 - 10-47 2 

 = \/30-47 x 9-53 = 17-04 



C = 31 34' 



B = 180 - (A + C) = 110 26' 

 AC = x+y= 30-44 



Case III. Let the base be 17 and the angles at the base 34 3 

 and 61. 



Then - = tan 34 = 0-6745 



x 



h = 



1 = tan 61 = 1-804, 

 17 x 



h = 30-67 - l-804tf 



