Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 68.01   b = 37.83   c = 42.15

Area: T = 714.1644282383
Perimeter: p = 147.99
Semiperimeter: s = 73.995

Angle ∠ A = α = 116.3933108909° = 116°23'35″ = 2.03114429771 rad
Angle ∠ B = β = 29.88550813738° = 29°53'6″ = 0.52215930672 rad
Angle ∠ C = γ = 33.72218097169° = 33°43'19″ = 0.58985566093 rad

Height: ha = 21.00217433431
Height: hb = 37.75765044876
Height: hc = 33.88767986896

Median: ma = 21.15548026462
Median: mb = 53.32217973722
Median: mc = 50.83438359265

Inradius: r = 9.65215208106
Circumradius: R = 37.96219556803

Vertex coordinates: A[42.15; 0] B[0; 0] C[58.96664733096; 33.88767986896]
Centroid: CG[33.70554911032; 11.29655995632]
Coordinates of the circumscribed circle: U[21.075; 31.57545855724]
Coordinates of the inscribed circle: I[36.165; 9.65215208106]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 63.60768910907° = 63°36'25″ = 2.03114429771 rad
∠ B' = β' = 150.1154918626° = 150°6'54″ = 0.52215930672 rad
∠ C' = γ' = 146.2788190283° = 146°16'41″ = 0.58985566093 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 = 68.01 ; ; b = 37.83 ; ; c = 42.15 ; ;

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

p = a+b+c = 68.01+37.83+42.15 = 147.99 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 147.99 }{ 2 } = 74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 74 * (74-68.01)(74-37.83)(74-42.15) } ; ; T = sqrt{ 510030.62 } = 714.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 714.16 }{ 68.01 } = 21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 714.16 }{ 37.83 } = 37.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 714.16 }{ 42.15 } = 33.89 ; ;

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{ 68.01**2-37.83**2-42.15**2 }{ 2 * 37.83 * 42.15 } ) = 116° 23'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 37.83**2-68.01**2-42.15**2 }{ 2 * 68.01 * 42.15 } ) = 29° 53'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 42.15**2-68.01**2-37.83**2 }{ 2 * 37.83 * 68.01 } ) = 33° 43'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 714.16 }{ 74 } = 9.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 68.01 }{ 2 * sin 116° 23'35" } = 37.96 ; ;




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