Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 989   b = 861   c = 673

Area: T = 284643.5687927
Perimeter: p = 2523
Semiperimeter: s = 1261.5

Angle ∠ A = α = 79.25217524559° = 79°15'6″ = 1.38332040183 rad
Angle ∠ B = β = 58.79332291994° = 58°47'36″ = 1.02661354274 rad
Angle ∠ C = γ = 41.95550183447° = 41°57'18″ = 0.73222532079 rad

Height: ha = 575.6198944241
Height: hb = 661.1932956857
Height: hc = 845.8954704092

Median: ma = 593.7976892885
Median: mb = 728.1454731492
Median: mc = 863.9965804388

Inradius: r = 225.6398975765
Circumradius: R = 503.333037663

Vertex coordinates: A[673; 0] B[0; 0] C[512.4298677563; 845.8954704092]
Centroid: CG[395.1432892521; 281.9654901364]
Coordinates of the circumscribed circle: U[336.5; 374.3121658967]
Coordinates of the inscribed circle: I[400.5; 225.6398975765]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100.7488247544° = 100°44'54″ = 1.38332040183 rad
∠ B' = β' = 121.2076770801° = 121°12'24″ = 1.02661354274 rad
∠ C' = γ' = 138.0454981655° = 138°2'42″ = 0.73222532079 rad

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How did we calculate this triangle?

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

a = 989 ; ; b = 861 ; ; c = 673 ; ;

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

p = a+b+c = 989+861+673 = 2523 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2523 }{ 2 } = 1261.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1261.5 * (1261.5-989)(1261.5-861)(1261.5-673) } ; ; T = sqrt{ 81021960762.2 } = 284643.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 284643.57 }{ 989 } = 575.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 284643.57 }{ 861 } = 661.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 284643.57 }{ 673 } = 845.89 ; ;

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{ 861**2+673**2-989**2 }{ 2 * 861 * 673 } ) = 79° 15'6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 989**2+673**2-861**2 }{ 2 * 989 * 673 } ) = 58° 47'36" ; ; gamma = 180° - alpha - beta = 180° - 79° 15'6" - 58° 47'36" = 41° 57'18" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 284643.57 }{ 1261.5 } = 225.64 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 989 }{ 2 * sin 79° 15'6" } = 503.33 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 861**2+2 * 673**2 - 989**2 } }{ 2 } = 593.797 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 673**2+2 * 989**2 - 861**2 } }{ 2 } = 728.145 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 861**2+2 * 989**2 - 673**2 } }{ 2 } = 863.996 ; ;
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