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

Calculate another triangle




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

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

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

2. Semiperimeter of the triangle

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

3. 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 ; ;

4. 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 ; ;

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

6. Inradius

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

7. Circumradius

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




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.