Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 19.65   b = 11.05   c = 20.88

Area: T = 107.0533123794
Perimeter: p = 51.58
Semiperimeter: s = 25.79

Angle ∠ A = α = 68.12114188325° = 68°7'17″ = 1.18989430498 rad
Angle ∠ B = β = 31.45656694687° = 31°27'20″ = 0.54990050006 rad
Angle ∠ C = γ = 80.42329116987° = 80°25'22″ = 1.40436446032 rad

Height: ha = 10.89659922437
Height: hb = 19.37661310034
Height: hc = 10.25441306316

Median: ma = 13.51095456992
Median: mb = 19.50769942585
Median: mc = 12.04765306209

Inradius: r = 4.15109547807
Circumradius: R = 10.58875626029

Vertex coordinates: A[20.88; 0] B[0; 0] C[16.76223180077; 10.25441306316]
Centroid: CG[12.54774393359; 3.41880435439]
Coordinates of the circumscribed circle: U[10.44; 1.7611499892]
Coordinates of the inscribed circle: I[14.74; 4.15109547807]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.8798581167° = 111°52'43″ = 1.18989430498 rad
∠ B' = β' = 148.5444330531° = 148°32'40″ = 0.54990050006 rad
∠ C' = γ' = 99.57770883013° = 99°34'38″ = 1.40436446032 rad

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How did we calculate this triangle?

a = 19.65 ; ; b = 11.05 ; ; c = 20.88 ; ;

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

p = a+b+c = 19.65+11.05+20.88 = 51.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51.58 }{ 2 } = 25.79 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.79 * (25.79-19.65)(25.79-11.05)(25.79-20.88) } ; ; T = sqrt{ 11460.37 } = 107.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.05 }{ 19.65 } = 10.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.05 }{ 11.05 } = 19.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.05 }{ 20.88 } = 10.25 ; ;

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{ 11.05**2+20.88**2-19.65**2 }{ 2 * 11.05 * 20.88 } ) = 68° 7'17" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 19.65**2+20.88**2-11.05**2 }{ 2 * 19.65 * 20.88 } ) = 31° 27'20" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 19.65**2+11.05**2-20.88**2 }{ 2 * 19.65 * 11.05 } ) = 80° 25'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.05 }{ 25.79 } = 4.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19.65 }{ 2 * sin 68° 7'17" } = 10.59 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.05**2+2 * 20.88**2 - 19.65**2 } }{ 2 } = 13.51 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20.88**2+2 * 19.65**2 - 11.05**2 } }{ 2 } = 19.507 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.05**2+2 * 19.65**2 - 20.88**2 } }{ 2 } = 12.047 ; ;
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