Triangle calculator

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

You have entered side a, b and c.

Obtuse isosceles triangle.

Sides: a = 19.5   b = 19.5   c = 32

Area: T = 178.3487974477
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 34.86438379543° = 34°51'50″ = 0.60884887622 rad
Angle ∠ B = β = 34.86438379543° = 34°51'50″ = 0.60884887622 rad
Angle ∠ C = γ = 110.2722324091° = 110°16'20″ = 1.92546151292 rad

Height: ha = 18.29220999463
Height: hb = 18.29220999463
Height: hc = 11.14767484048

Median: ma = 24.63986383552
Median: mb = 24.63986383552
Median: mc = 11.14767484048

Inradius: r = 5.0243886605
Circumradius: R = 17.05765435852

Vertex coordinates: A[32; 0] B[0; 0] C[16; 11.14767484048]
Centroid: CG[16; 3.71655828016]
Coordinates of the circumscribed circle: U[16; -5.91097951804]
Coordinates of the inscribed circle: I[16; 5.0243886605]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.1366162046° = 145°8'10″ = 0.60884887622 rad
∠ B' = β' = 145.1366162046° = 145°8'10″ = 0.60884887622 rad
∠ C' = γ' = 69.72876759086° = 69°43'40″ = 1.92546151292 rad

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How did we calculate this triangle?

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

a = 19.5 ; ; b = 19.5 ; ; c = 32 ; ;

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

p = a+b+c = 19.5+19.5+32 = 71 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-19.5)(35.5-19.5)(35.5-32) } ; ; T = sqrt{ 31808 } = 178.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 178.35 }{ 19.5 } = 18.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 178.35 }{ 19.5 } = 18.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 178.35 }{ 32 } = 11.15 ; ;

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{ 19.5**2+32**2-19.5**2 }{ 2 * 19.5 * 32 } ) = 34° 51'50" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 19.5**2+32**2-19.5**2 }{ 2 * 19.5 * 32 } ) = 34° 51'50" ; ; gamma = 180° - alpha - beta = 180° - 34° 51'50" - 34° 51'50" = 110° 16'20" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 178.35 }{ 35.5 } = 5.02 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 19.5 }{ 2 * sin 34° 51'50" } = 17.06 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.5**2+2 * 32**2 - 19.5**2 } }{ 2 } = 24.639 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 19.5**2 - 19.5**2 } }{ 2 } = 24.639 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.5**2+2 * 19.5**2 - 32**2 } }{ 2 } = 11.147 ; ;
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