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