Illustration 2: Show that the triangle is obtuse angled when sides of triangle 3x+4y, 4x+3y, 5x+5y units where x, y>0. Ans: Let a= 3x+4y b= 4x+3y c= 5x+5y Since x, y>0 so c is largest side and angle C will be largest angle. So, 
Now since x, y>0 So, Cos C<0 And thus angle C is obtuse. Projection Formula: 1) a = bCosC + cCosB 2) b = cCosA + aCosC 3) c = aCosB + bCosA
How?  Fig (5) Let us draw a perpendicular line from C on Side AB So, AB=BD+AD 
Illustration 3:
Drive Projection formula using the Cosine Rule Ans: 
Napier Analogy: 
How? 
Illustration 4: If in a triangle ABC, a = 6, b = 3, and Cos (A-B) = 4/5 then find the angle C. Ans: Cos (A-B) = 4/5 
Componendo and dividendo: 
Trigonometric ratios of half angles: 
How? 
Since A is angle of triangle, so 0<A<180 and thus A/2 is acute. So, Sin A/2 has to be +ve and thus  
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