Triangle Basic Formulas Identities

Basic Triangle Formulas & Identities

Area of Triangle = ½ (Any Side) × (Corresponding Altitude)

Heron’s Formula

∆ =√(s(s – a)(s – b)(s – c))

S = ½ (a + b + c)…….. Semi-Perimeter

Where a, b, c……sides of a ∆

Area of an Equilateral Triangle (∆)

Area= (√3a²)/4

Centroid (G) of a Triangle

G = ({x₁+ x₂+ x₃ /3};  {y₁ + y₂ + y₃} /3 )

Area = ½ [x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

Length of Medians of a Triangle

 L₁ = ½ (√(2b² + 2c² – a²)  )

L₂ = ½ (√(2c² + 2a² – b²)  )

L3 = ½ (√(2a² + 2b² – c²)

4(L₁² + L₂² + L₃²) = 3(a² + b² + c²)

Length of Angle Bisector (x)

x = (2bc/ (b + c)) cos (A/2)

Theory: Mensuration

Sine Rule

a/sin A = b/sin B = c/sin C = 2R

Where R is radius of Circumcircle

Cosine Rule

Cos A = (b² + c² – a²)/2bc

Cos B = (c² + a² – b²)/2ca

Cos C = (a² + b² – c²)/2ab

Area (Δ)

∆ = 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B

∆ = abc/4R

r = ∆ /s

Where R = Circumcircle Radius

   r = Incircle radius

Projection Formula

a = b cos C + c cos B

b = c cos A + a cos C

c = a cos B + b cos A

Profit And Loss Important Formulas

Tangent Rule

tan ((B – C)/2)  = (b – c)/(b + c) cot (A/2)

tan ((C – A)/2 ) = (c – a)/(c + a) cot (B/2)

tan ((A – B)/2)  = (a – b)/(a + b) cot (C/2)

M-N Theorem

(m + n) cot θ = m cot α – n cot β

(m + n) cot θ = m cot B – n cot C

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