solution-of-triangles-2

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