Triangle calculator

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

You have entered side a, b and perimeter p.

Obtuse scalene triangle.

Sides: a = 11.2   b = 6.5   c = 8.3

Area: T = 26.73770529416
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 97.61658228711° = 97°36'57″ = 1.70437175111 rad
Angle ∠ B = β = 35.11662871715° = 35°6'59″ = 0.61328948322 rad
Angle ∠ C = γ = 47.26878899574° = 47°16'4″ = 0.82549803102 rad

Height: ha = 4.77444737396
Height: hb = 8.22767855205
Height: hc = 6.44326633594

Median: ma = 4.92203658401
Median: mb = 9.30660464215
Median: mc = 8.16222607162

Inradius: r = 2.05766963801
Circumradius: R = 5.65498373374

Vertex coordinates: A[8.3; 0] B[0; 0] C[9.16114457831; 6.44326633594]
Centroid: CG[5.82204819277; 2.14875544531]
Coordinates of the circumscribed circle: U[4.15; 3.83438181932]
Coordinates of the inscribed circle: I[6.5; 2.05766963801]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 82.38441771289° = 82°23'3″ = 1.70437175111 rad
∠ B' = β' = 144.8843712829° = 144°53'1″ = 0.61328948322 rad
∠ C' = γ' = 132.7322110043° = 132°43'56″ = 0.82549803102 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and perimeter p.

a = 11.2 ; ; b = 6.5 ; ; p = 26 ; ;


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 = 11.2 ; ; b = 6.5 ; ; c = 8.3 ; ;

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

p = a+b+c = 11.2+6.5+8.3 = 26 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-11.2)(13-6.5)(13-8.3) } ; ; T = sqrt{ 714.87 } = 26.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.74 }{ 11.2 } = 4.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.74 }{ 6.5 } = 8.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.74 }{ 8.3 } = 6.44 ; ;

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{ 6.5**2+8.3**2-11.2**2 }{ 2 * 6.5 * 8.3 } ) = 97° 36'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11.2**2+8.3**2-6.5**2 }{ 2 * 11.2 * 8.3 } ) = 35° 6'59" ; ; gamma = 180° - alpha - beta = 180° - 97° 36'57" - 35° 6'59" = 47° 16'4" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.74 }{ 13 } = 2.06 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11.2 }{ 2 * sin 97° 36'57" } = 5.65 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.5**2+2 * 8.3**2 - 11.2**2 } }{ 2 } = 4.92 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.3**2+2 * 11.2**2 - 6.5**2 } }{ 2 } = 9.306 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.5**2+2 * 11.2**2 - 8.3**2 } }{ 2 } = 8.162 ; ;
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