Triangle calculator - result

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered median ma, median mb and median mc.

Obtuse scalene triangle.

Sides: a = 2.94439202888   b = 1.29109944487   c = 2.16602468995

Area: T = 1.26765570128
Perimeter: p = 6.3955161637
Semiperimeter: s = 3.19875808185

Angle ∠ A = α = 114.7299199063° = 114°43'45″ = 2.00224022718 rad
Angle ∠ B = β = 23.47328053046° = 23°28'22″ = 0.41096777372 rad
Angle ∠ C = γ = 41.79879956322° = 41°47'53″ = 0.73295126445 rad

Height: ha = 0.86604560508
Height: hb = 1.9622141687
Height: hc = 1.173260394

Median: ma = 1
Median: mb = 2.5
Median: mc = 2

Inradius: r = 0.39660985147
Circumradius: R = 1.62105747827

Vertex coordinates: A[2.16602468995; 0] B[0; 0] C[2.77003086243; 1.173260394]
Centroid: CG[1.62201851746; 0.391086798]
Coordinates of the circumscribed circle: U[1.08801234497; 1.20881373927]
Coordinates of the inscribed circle: I[1.90765863698; 0.39660985147]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 65.27108009368° = 65°16'15″ = 2.00224022718 rad
∠ B' = β' = 156.5277194695° = 156°31'38″ = 0.41096777372 rad
∠ C' = γ' = 138.2022004368° = 138°12'7″ = 0.73295126445 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 2.94 ; ; b = 1.29 ; ; c = 2.16 ; ;

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

p = a+b+c = 2.94+1.29+2.16 = 6.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.4 }{ 2 } = 3.2 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.2 * (3.2-2.94)(3.2-1.29)(3.2-2.16) } ; ; T = sqrt{ 1.6 } = 1.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.27 }{ 2.94 } = 0.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.27 }{ 1.29 } = 1.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.27 }{ 2.16 } = 1.17 ; ;

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{ 2.94**2-1.29**2-2.16**2 }{ 2 * 1.29 * 2.16 } ) = 114° 43'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.29**2-2.94**2-2.16**2 }{ 2 * 2.94 * 2.16 } ) = 23° 28'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.16**2-2.94**2-1.29**2 }{ 2 * 1.29 * 2.94 } ) = 41° 47'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.27 }{ 3.2 } = 0.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.94 }{ 2 * sin 114° 43'45" } = 1.62 ; ;




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