Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37.7   b = 35.3   c = 3.03

Area: T = 33.72655181198
Perimeter: p = 76.03
Semiperimeter: s = 38.015

Angle ∠ A = α = 140.904373939° = 140°54'13″ = 2.45992341807 rad
Angle ∠ B = β = 36.19110252551° = 36°11'28″ = 0.63216525504 rad
Angle ∠ C = γ = 2.90552353546° = 2°54'19″ = 0.05107059225 rad

Height: ha = 1.78991521549
Height: hb = 1.91107942278
Height: hc = 22.26110680659

Median: ma = 16.50219074655
Median: mb = 20.09326093378
Median: mc = 36.48882827083

Inradius: r = 0.88771634386
Circumradius: R = 29.89109736959

Vertex coordinates: A[3.03; 0] B[0; 0] C[30.42658910891; 22.26110680659]
Centroid: CG[11.15219636964; 7.4220356022]
Coordinates of the circumscribed circle: U[1.515; 29.85325557279]
Coordinates of the inscribed circle: I[2.715; 0.88771634386]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 39.09662606097° = 39°5'47″ = 2.45992341807 rad
∠ B' = β' = 143.8098974745° = 143°48'32″ = 0.63216525504 rad
∠ C' = γ' = 177.0954764645° = 177°5'41″ = 0.05107059225 rad

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How did we calculate this triangle?

a = 37.7 ; ; b = 35.3 ; ; c = 3.03 ; ;

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

p = a+b+c = 37.7+35.3+3.03 = 76.03 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76.03 }{ 2 } = 38.02 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.02 * (38.02-37.7)(38.02-35.3)(38.02-3.03) } ; ; T = sqrt{ 1137.41 } = 33.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.73 }{ 37.7 } = 1.79 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.73 }{ 35.3 } = 1.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.73 }{ 3.03 } = 22.26 ; ;

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+3.03**2-37.7**2 }{ 2 * 35.3 * 3.03 } ) = 140° 54'13" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37.7**2+3.03**2-35.3**2 }{ 2 * 37.7 * 3.03 } ) = 36° 11'28" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 37.7**2+35.3**2-3.03**2 }{ 2 * 37.7 * 35.3 } ) = 2° 54'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.73 }{ 38.02 } = 0.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 37.7 }{ 2 * sin 140° 54'13" } = 29.89 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 35.3**2+2 * 3.03**2 - 37.7**2 } }{ 2 } = 16.502 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.03**2+2 * 37.7**2 - 35.3**2 } }{ 2 } = 20.093 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 35.3**2+2 * 37.7**2 - 3.03**2 } }{ 2 } = 36.488 ; ;
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