7.8 4.2 3.9 triangle

Obtuse scalene triangle.

Sides: a = 7.8   b = 4.2   c = 3.9

Area: T = 4.25657130719
Perimeter: p = 15.9
Semiperimeter: s = 7.95

Angle ∠ A = α = 148.6933027773° = 148°41'35″ = 2.59551829094 rad
Angle ∠ B = β = 16.24880921657° = 16°14'53″ = 0.28435827055 rad
Angle ∠ C = γ = 15.05988800618° = 15°3'32″ = 0.26328270387 rad

Height: ha = 1.091120848
Height: hb = 2.02765300342
Height: hc = 2.18224169599

Median: ma = 1.10222703843
Median: mb = 5.7987844427
Median: mc = 5.95329404499

Inradius: r = 0.53553098204
Circumradius: R = 7.50554402072

Vertex coordinates: A[3.9; 0] B[0; 0] C[7.48884615385; 2.18224169599]
Centroid: CG[3.79661538462; 0.727747232]
Coordinates of the circumscribed circle: U[1.95; 7.24876984419]
Coordinates of the inscribed circle: I[3.75; 0.53553098204]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 31.30769722275° = 31°18'25″ = 2.59551829094 rad
∠ B' = β' = 163.7521907834° = 163°45'7″ = 0.28435827055 rad
∠ C' = γ' = 164.9411119938° = 164°56'28″ = 0.26328270387 rad

Calculate another triangle




How did we calculate this triangle?

a = 7.8 ; ; b = 4.2 ; ; c = 3.9 ; ;

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

p = a+b+c = 7.8+4.2+3.9 = 15.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.9 }{ 2 } = 7.95 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.95 * (7.95-7.8)(7.95-4.2)(7.95-3.9) } ; ; T = sqrt{ 18.11 } = 4.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.26 }{ 7.8 } = 1.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.26 }{ 4.2 } = 2.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.26 }{ 3.9 } = 2.18 ; ;

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{ 7.8**2-4.2**2-3.9**2 }{ 2 * 4.2 * 3.9 } ) = 148° 41'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.2**2-7.8**2-3.9**2 }{ 2 * 7.8 * 3.9 } ) = 16° 14'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.9**2-7.8**2-4.2**2 }{ 2 * 4.2 * 7.8 } ) = 15° 3'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.26 }{ 7.95 } = 0.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.8 }{ 2 * sin 148° 41'35" } = 7.51 ; ;




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