Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 22.01   b = 20   c = 35.65

Area: T = 197.7598614618
Perimeter: p = 77.66
Semiperimeter: s = 38.83

Angle ∠ A = α = 33.6921611776° = 33°41'30″ = 0.58880295558 rad
Angle ∠ B = β = 30.26992497232° = 30°16'9″ = 0.52882980698 rad
Angle ∠ C = γ = 116.0399138501° = 116°2'21″ = 2.0255265028 rad

Height: ha = 17.97698877436
Height: hb = 19.77658614618
Height: hc = 11.0944452433

Median: ma = 26.72773497564
Median: mb = 27.88769378025
Median: mc = 11.15774829151

Inradius: r = 5.09329336755
Circumradius: R = 19.83987438523

Vertex coordinates: A[35.65; 0] B[0; 0] C[19.00992931276; 11.0944452433]
Centroid: CG[18.22197643759; 3.6988150811]
Coordinates of the circumscribed circle: U[17.825; -8.70989111052]
Coordinates of the inscribed circle: I[18.83; 5.09329336755]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3088388224° = 146°18'30″ = 0.58880295558 rad
∠ B' = β' = 149.7310750277° = 149°43'51″ = 0.52882980698 rad
∠ C' = γ' = 63.96108614993° = 63°57'39″ = 2.0255265028 rad

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How did we calculate this triangle?

a = 22.01 ; ; b = 20 ; ; c = 35.65 ; ;

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

p = a+b+c = 22.01+20+35.65 = 77.66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77.66 }{ 2 } = 38.83 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.83 * (38.83-22.01)(38.83-20)(38.83-35.65) } ; ; T = sqrt{ 39108.47 } = 197.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.76 }{ 22.01 } = 17.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.76 }{ 20 } = 19.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.76 }{ 35.65 } = 11.09 ; ;

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{ 20**2+35.65**2-22.01**2 }{ 2 * 20 * 35.65 } ) = 33° 41'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 22.01**2+35.65**2-20**2 }{ 2 * 22.01 * 35.65 } ) = 30° 16'9" ; ; gamma = 180° - alpha - beta = 180° - 33° 41'30" - 30° 16'9" = 116° 2'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.76 }{ 38.83 } = 5.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 22.01 }{ 2 * sin 33° 41'30" } = 19.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 35.65**2 - 22.01**2 } }{ 2 } = 26.727 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 35.65**2+2 * 22.01**2 - 20**2 } }{ 2 } = 27.887 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 22.01**2 - 35.65**2 } }{ 2 } = 11.157 ; ;
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