1.3 0.5 1.2 triangle

Right scalene triangle.

Sides: a = 1.3   b = 0.5   c = 1.2

Area: T = 0.3
Perimeter: p = 3
Semiperimeter: s = 1.5

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ C = γ = 67.3880135052° = 67°22'49″ = 1.17660052071 rad

Height: ha = 0.46215384615
Height: hb = 1.2
Height: hc = 0.5

Median: ma = 0.65
Median: mb = 1.22657650672
Median: mc = 0.78110249676

Inradius: r = 0.2
Circumradius: R = 0.65

Vertex coordinates: A[1.2; 0] B[0; 0] C[1.2; 0.5]
Centroid: CG[0.8; 0.16766666667]
Coordinates of the circumscribed circle: U[0.6; 0.25]
Coordinates of the inscribed circle: I[1; 0.2]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ C' = γ' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad

Calculate another triangle




How did we calculate this triangle?

a = 1.3 ; ; b = 0.5 ; ; c = 1.2 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 1.3+0.5+1.2 = 3 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3 }{ 2 } = 1.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.5 * (1.5-1.3)(1.5-0.5)(1.5-1.2) } ; ; T = sqrt{ 0.09 } = 0.3 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.3 }{ 1.3 } = 0.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.3 }{ 0.5 } = 1.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.3 }{ 1.2 } = 0.5 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 1.3**2-0.5**2-1.2**2 }{ 2 * 0.5 * 1.2 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.5**2-1.3**2-1.2**2 }{ 2 * 1.3 * 1.2 } ) = 22° 37'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.2**2-1.3**2-0.5**2 }{ 2 * 0.5 * 1.3 } ) = 67° 22'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.3 }{ 1.5 } = 0.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.3 }{ 2 * sin 90° } = 0.65 ; ;




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