Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37.7   b = 35.3   c = 57.81

Area: T = 643.6776653201
Perimeter: p = 130.81
Semiperimeter: s = 65.405

Angle ∠ A = α = 39.11222151414° = 39°6'44″ = 0.6832636932 rad
Angle ∠ B = β = 36.20553906274° = 36°12'19″ = 0.63219032734 rad
Angle ∠ C = γ = 104.6822394231° = 104°40'57″ = 1.82770524482 rad

Height: ha = 34.14773025571
Height: hb = 36.46989321927
Height: hc = 22.26986958381

Median: ma = 44.03109044876
Median: mb = 45.49985774503
Median: mc = 22.32201920915

Inradius: r = 9.84113982601
Circumradius: R = 29.88107350389

Vertex coordinates: A[57.81; 0] B[0; 0] C[30.42203087701; 22.26986958381]
Centroid: CG[29.41101029234; 7.42328986127]
Coordinates of the circumscribed circle: U[28.905; -7.5743592375]
Coordinates of the inscribed circle: I[30.105; 9.84113982601]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.8887784859° = 140°53'16″ = 0.6832636932 rad
∠ B' = β' = 143.7954609373° = 143°47'41″ = 0.63219032734 rad
∠ C' = γ' = 75.31876057688° = 75°19'3″ = 1.82770524482 rad

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How did we calculate this triangle?

a = 37.7 ; ; b = 35.3 ; ; c = 57.81 ; ;

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

p = a+b+c = 37.7+35.3+57.81 = 130.81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 130.81 }{ 2 } = 65.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.41 * (65.41-37.7)(65.41-35.3)(65.41-57.81) } ; ; T = sqrt{ 414319.63 } = 643.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 643.68 }{ 37.7 } = 34.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 643.68 }{ 35.3 } = 36.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 643.68 }{ 57.81 } = 22.27 ; ;

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{ 35.3**2+57.81**2-37.7**2 }{ 2 * 35.3 * 57.81 } ) = 39° 6'44" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.7**2+57.81**2-35.3**2 }{ 2 * 37.7 * 57.81 } ) = 36° 12'19" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 37.7**2+35.3**2-57.81**2 }{ 2 * 37.7 * 35.3 } ) = 104° 40'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 643.68 }{ 65.41 } = 9.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 37.7 }{ 2 * sin 39° 6'44" } = 29.88 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 35.3**2+2 * 57.81**2 - 37.7**2 } }{ 2 } = 44.031 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 57.81**2+2 * 37.7**2 - 35.3**2 } }{ 2 } = 45.499 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 35.3**2+2 * 37.7**2 - 57.81**2 } }{ 2 } = 22.32 ; ;
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