ANGLES GREATER THAN 90 



28 



Then 



0-6745# - 80-67 - l-804a? 

 2-479z - 80-67 

 x - 12-87 

 x 

 AB 



12-37 



AB 



17 -,r 

 BC 



BC 



cos 84 - 0-8290 

 = 14-92 



0-8290 

 cos 61 = 0-4848 

 4-63 



0-4848 



= 9-550 



JC . -1 



FIG. 6. 



I7-X- 



iC 



12. Angles greater than 90. In order to find the trigono- 

 metrical ratios of a given acute angle, we make that angle the 

 base angle of a right-angled triangle ; but when we have to deal 

 with an angle greater than 90, we cannot treat it in the same 

 way, since the base angle of a right-angled triangle must be acute. 



If we look upon an angle as being measured by the amount of 

 rotation of a line with reference to a fixed line, then we can con- 

 sider one arm of an angle to occupy a fixed position, while the 

 other arm can be taken as a movable arm rotating with reference 

 to the fixed arm. If we take a point on the movable arm and 

 from that point draw a perpendicular to the fixed arm, we shall 

 obtafn a right-angled triangle which in some way will enable us 

 to determine the trigonometrical ratios of the angle between the 

 two arms. 



For angles between and 360 there are four cases to be 

 considered, depending upon the position of the moving arm. 



Case I. When the angle lies between and 90. 

 Case II. When the angle lies between 90 and 180. 

 Case III. When the angle lies between 180 and 270. 

 Case IV. When the angle lies between 270 and 360. 



