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 = 60   b = 107   c = 125

Area: T = 3206.768846685
Perimeter: p = 292
Semiperimeter: s = 146

Angle ∠ A = α = 28.65438469175° = 28°39'14″ = 0.55001039721 rad
Angle ∠ B = β = 58.7755012269° = 58°46'30″ = 1.0265817482 rad
Angle ∠ C = γ = 92.57111408135° = 92°34'16″ = 1.61656711995 rad

Height: ha = 106.8922282228
Height: hb = 59.94395975113
Height: hc = 51.30882954696

Median: ma = 112.4144411887
Median: mb = 82.16599050632
Median: mc = 60.15218910758

Inradius: r = 21.96441675812
Circumradius: R = 62.56329826643

Vertex coordinates: A[125; 0] B[0; 0] C[31.104; 51.30882954696]
Centroid: CG[52.03546666667; 17.10327651565]
Coordinates of the circumscribed circle: U[62.5; -2.80765637083]
Coordinates of the inscribed circle: I[39; 21.96441675812]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.3466153083° = 151°20'46″ = 0.55001039721 rad
∠ B' = β' = 121.2254987731° = 121°13'30″ = 1.0265817482 rad
∠ C' = γ' = 87.42988591865° = 87°25'44″ = 1.61656711995 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 60 ; ; b = 107 ; ; c = 125 ; ;


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 = 60 ; ; b = 107 ; ; c = 125 ; ; : Nr. 1

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

p = a+b+c = 60+107+125 = 292 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 292 }{ 2 } = 146 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 146 * (146-60)(146-107)(146-125) } ; ; T = sqrt{ 10283364 } = 3206.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3206.77 }{ 60 } = 106.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3206.77 }{ 107 } = 59.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3206.77 }{ 125 } = 51.31 ; ;

6. 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 107**2+125**2-60**2 }{ 2 * 107 * 125 } ) = 28° 39'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 60**2+125**2-107**2 }{ 2 * 60 * 125 } ) = 58° 46'30" ; ; gamma = 180° - alpha - beta = 180° - 28° 39'14" - 58° 46'30" = 92° 34'16" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3206.77 }{ 146 } = 21.96 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 28° 39'14" } = 62.56 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 107**2+2 * 125**2 - 60**2 } }{ 2 } = 112.414 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 60**2 - 107**2 } }{ 2 } = 82.16 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 107**2+2 * 60**2 - 125**2 } }{ 2 } = 60.152 ; ;
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