Triangle calculator

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

You have entered height ha, height hb and height hc.

Obtuse scalene triangle.

Sides: a = 6.69215220599   b = 5.0198641545   c = 4.0154913236

Area: T = 10.03772830899
Perimeter: p = 15.72550768409
Semiperimeter: s = 7.86325384204

Angle ∠ A = α = 94.94399211322° = 94°56'24″ = 1.65770142153 rad
Angle ∠ B = β = 48.35496321995° = 48°20'59″ = 0.8443860274 rad
Angle ∠ C = γ = 36.71104466683° = 36°42'38″ = 0.64107181642 rad

Height: ha = 3
Height: hb = 4
Height: hc = 5

Median: ma = 3.07655534063
Median: mb = 4.91443979434
Median: mc = 5.56334281828

Inradius: r = 1.27765957447
Circumradius: R = 3.35882350609

Vertex coordinates: A[4.0154913236; 0] B[0; 0] C[4.44770740357; 5]
Centroid: CG[2.82106624239; 1.66766666667]
Coordinates of the circumscribed circle: U[2.0077456618; 2.69221851072]
Coordinates of the inscribed circle: I[2.84438968755; 1.27765957447]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 85.06600788678° = 85°3'36″ = 1.65770142153 rad
∠ B' = β' = 131.65503678° = 131°39'1″ = 0.8443860274 rad
∠ C' = γ' = 143.2989553332° = 143°17'22″ = 0.64107181642 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 = 6.69 ; ; b = 5.02 ; ; c = 4.01 ; ;

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

p = a+b+c = 6.69+5.02+4.01 = 15.73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.73 }{ 2 } = 7.86 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.86 * (7.86-6.69)(7.86-5.02)(7.86-4.01) } ; ; T = sqrt{ 100.75 } = 10.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.04 }{ 6.69 } = 3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.04 }{ 5.02 } = 4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.04 }{ 4.01 } = 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{ 6.69**2-5.02**2-4.01**2 }{ 2 * 5.02 * 4.01 } ) = 94° 56'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.02**2-6.69**2-4.01**2 }{ 2 * 6.69 * 4.01 } ) = 48° 20'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.01**2-6.69**2-5.02**2 }{ 2 * 5.02 * 6.69 } ) = 36° 42'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.04 }{ 7.86 } = 1.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.69 }{ 2 * sin 94° 56'24" } = 3.36 ; ;




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