Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 19.04   b = 18.75   c = 3.31

Area: T = 31.03112499909
Perimeter: p = 41.1
Semiperimeter: s = 20.55

Angle ∠ A = α = 90.00113847923° = 90°5″ = 1.5710820496 rad
Angle ∠ B = β = 79.98771908433° = 79°59'14″ = 1.39660398396 rad
Angle ∠ C = γ = 10.01114243645° = 10°41″ = 0.1754732318 rad

Height: ha = 3.26595850831
Height: hb = 3.3109999999
Height: hc = 18.75499999945

Median: ma = 9.52199212182
Median: mb = 9.94222444649
Median: mc = 18.82329387982

Inradius: r = 1.51100364959
Circumradius: R = 9.52200000028

Vertex coordinates: A[3.31; 0] B[0; 0] C[3.31104531722; 18.75499999945]
Centroid: CG[2.20768177241; 6.25499999982]
Coordinates of the circumscribed circle: U[1.655; 9.37550400027]
Coordinates of the inscribed circle: I[1.8; 1.51100364959]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99986152077° = 89°59'55″ = 1.5710820496 rad
∠ B' = β' = 100.0132809157° = 100°46″ = 1.39660398396 rad
∠ C' = γ' = 169.9898575636° = 169°59'19″ = 0.1754732318 rad

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How did we calculate this triangle?

a = 19.04 ; ; b = 18.75 ; ; c = 3.31 ; ;

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

p = a+b+c = 19.04+18.75+3.31 = 41.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41.1 }{ 2 } = 20.55 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.55 * (20.55-19.04)(20.55-18.75)(20.55-3.31) } ; ; T = sqrt{ 962.94 } = 31.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.03 }{ 19.04 } = 3.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.03 }{ 18.75 } = 3.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.03 }{ 3.31 } = 18.75 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 19.04**2-18.75**2-3.31**2 }{ 2 * 18.75 * 3.31 } ) = 90° 5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18.75**2-19.04**2-3.31**2 }{ 2 * 19.04 * 3.31 } ) = 79° 59'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.31**2-19.04**2-18.75**2 }{ 2 * 18.75 * 19.04 } ) = 10° 41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.03 }{ 20.55 } = 1.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19.04 }{ 2 * sin 90° 5" } = 9.52 ; ;

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