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 = 1.6   b = 2.6   c = 4.1

Area: T = 0.9065617883
Perimeter: p = 8.3
Semiperimeter: s = 4.15

Angle ∠ A = α = 9.78325599442° = 9°46'57″ = 0.17107378803 rad
Angle ∠ B = β = 16.02877573234° = 16°1'40″ = 0.2879737137 rad
Angle ∠ C = γ = 154.1989682732° = 154°11'23″ = 2.69111176363 rad

Height: ha = 1.13220223537
Height: hb = 0.69766291408
Height: hc = 0.4421764821

Median: ma = 3.33884127965
Median: mb = 2.82875431031
Median: mc = 0.67663874629

Inradius: r = 0.21882211766
Circumradius: R = 4.70883875883

Vertex coordinates: A[4.1; 0] B[0; 0] C[1.5387804878; 0.4421764821]
Centroid: CG[1.87992682927; 0.14772549403]
Coordinates of the circumscribed circle: U[2.05; -4.23986806534]
Coordinates of the inscribed circle: I[1.55; 0.21882211766]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.2177440056° = 170°13'3″ = 0.17107378803 rad
∠ B' = β' = 163.9722242677° = 163°58'20″ = 0.2879737137 rad
∠ C' = γ' = 25.81103172677° = 25°48'37″ = 2.69111176363 rad

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How did we calculate this triangle?

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

a = 1.6 ; ; b = 2.6 ; ; c = 4.1 ; ;


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 = 1.6 ; ; b = 2.6 ; ; c = 4.1 ; ; : Nr. 1

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

p = a+b+c = 1.6+2.6+4.1 = 8.3 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.3 }{ 2 } = 4.15 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.15 * (4.15-1.6)(4.15-2.6)(4.15-4.1) } ; ; T = sqrt{ 0.82 } = 0.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.91 }{ 1.6 } = 1.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.91 }{ 2.6 } = 0.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.91 }{ 4.1 } = 0.44 ; ;

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{ 2.6**2+4.1**2-1.6**2 }{ 2 * 2.6 * 4.1 } ) = 9° 46'57" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.6**2+4.1**2-2.6**2 }{ 2 * 1.6 * 4.1 } ) = 16° 1'40" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 1.6**2+2.6**2-4.1**2 }{ 2 * 1.6 * 2.6 } ) = 154° 11'23" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.91 }{ 4.15 } = 0.22 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.6 }{ 2 * sin 9° 46'57" } = 4.71 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.6**2+2 * 4.1**2 - 1.6**2 } }{ 2 } = 3.338 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.1**2+2 * 1.6**2 - 2.6**2 } }{ 2 } = 2.828 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.6**2+2 * 1.6**2 - 4.1**2 } }{ 2 } = 0.676 ; ;
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