28 PRACTICAL MATHEMATICS 



But h* = c 2 -x*= (c+x)(c-x) 



2ac + a 2 + c z - b z \/2ac - a 2 - c 2 + 



-*T "A- -25" 



= -1 V{(a+ c) 2 - b*}{b 2 - (a-c) 2 } 



ad 



= Via + b + c)(a b + c)(a + b - c)(b a + c) 



Lid 



d)(s b) (s c) 

 where 2s = a + b + c the perimeter of the triangle 



Then h = - Vs(s - a) (s - b)(s - c) 





This is the perpendicular drawn to the side a. It can be easily 

 shown that the other two perpendiculars are 



h 6 = -r Vs(s -a)(s - b) (s - c) 



h c = - Vs(s d)(s b)(s c) 



The area of the triangle = - ah 



= VXs a)(s b) (s c) 



16. The Compound Angle. It is sometimes necessary to express 

 the trigonometrical ratios of the sum or difference of two given 

 angles in terms of the trigonometrical ratios of those angles. 

 /\ /\ 



Let POM = A and POR = B, the angles being measured in anti- 

 clockwise direction in the first case, thus producing the compound 

 angle ROM = A + B, and in the second case B is measured in 



