Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 14.2   b = 6.73   c = 19.31

Area: T = 35.9422446875
Perimeter: p = 40.24
Semiperimeter: s = 20.12

Angle ∠ A = α = 33.58331562132° = 33°34'59″ = 0.58661366491 rad
Angle ∠ B = β = 15.19882886843° = 15°11'54″ = 0.26552601782 rad
Angle ∠ C = γ = 131.2198555102° = 131°13'7″ = 2.29901958262 rad

Height: ha = 5.06223164613
Height: hb = 10.68112620728
Height: hc = 3.72326770456

Median: ma = 12.59766066859
Median: mb = 16.6111286073
Median: mc = 5.54997659041

Inradius: r = 1.78664039202
Circumradius: R = 12.83656554746

Vertex coordinates: A[19.31; 0] B[0; 0] C[13.70333454169; 3.72326770456]
Centroid: CG[11.00444484723; 1.24108923485]
Coordinates of the circumscribed circle: U[9.655; -8.45878381672]
Coordinates of the inscribed circle: I[13.39; 1.78664039202]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4176843787° = 146°25'1″ = 0.58661366491 rad
∠ B' = β' = 164.8021711316° = 164°48'6″ = 0.26552601782 rad
∠ C' = γ' = 48.78114448975° = 48°46'53″ = 2.29901958262 rad

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How did we calculate this triangle?

a = 14.2 ; ; b = 6.73 ; ; c = 19.31 ; ;

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

p = a+b+c = 14.2+6.73+19.31 = 40.24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40.24 }{ 2 } = 20.12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.12 * (20.12-14.2)(20.12-6.73)(20.12-19.31) } ; ; T = sqrt{ 1291.86 } = 35.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.94 }{ 14.2 } = 5.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.94 }{ 6.73 } = 10.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.94 }{ 19.31 } = 3.72 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 6.73**2+19.31**2-14.2**2 }{ 2 * 6.73 * 19.31 } ) = 33° 34'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14.2**2+19.31**2-6.73**2 }{ 2 * 14.2 * 19.31 } ) = 15° 11'54" ; ; gamma = 180° - alpha - beta = 180° - 33° 34'59" - 15° 11'54" = 131° 13'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.94 }{ 20.12 } = 1.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14.2 }{ 2 * sin 33° 34'59" } = 12.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.73**2+2 * 19.31**2 - 14.2**2 } }{ 2 } = 12.597 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19.31**2+2 * 14.2**2 - 6.73**2 } }{ 2 } = 16.611 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.73**2+2 * 14.2**2 - 19.31**2 } }{ 2 } = 5.5 ; ;
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