Solution OF Triangle

Basic Rules :

In a triangle ABC, the angles are denoted by capital letters A,B, and C and the lengths of the sides opposite to these angles are denoted by small letters a, b, and c respectively. Semi – perimeter of the triangle is written as  s = (a + b + c)/2 and its area denoted by S or Δ .

Sine rule:

, where R is the radius of the circumcircle of the Δ ABC.

Cosine rule:

Projection rule:

a = b cosC + c cosB ,

b = c cosA + a cosC ,

c = a cosB + b cosA

Napier’s analogy :

Solutions of triangle : m-n theorem

If in a triangle ABC, D is a point on the line BC such that BD:DC = m : n and ∠ADC = θ , ∠BAD = α , ∠DAC = β , then

(a) (m + n)cotθ = m cotα – n cotβ

(b) (m + n)cotθ = n cotB – m cotC

Auxiliary formulae:

Trigonometric ratios of half – angles:


Area of a triangle:

where R and r are the radii of the circumcircle and the incircle of the Δ ABC respectively.

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