Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 38   b = 42   c = 55.69

Area: T = 797.5554674613
Perimeter: p = 135.69
Semiperimeter: s = 67.845

Angle ∠ A = α = 42.9987616102° = 42°59'51″ = 0.75504499715 rad
Angle ∠ B = β = 48.91766182705° = 48°55' = 0.85437560478 rad
Angle ∠ C = γ = 88.08657656275° = 88°5'9″ = 1.53773866343 rad

Height: ha = 41.97765618217
Height: hb = 37.97987940292
Height: hc = 28.64326530656

Median: ma = 45.5165800004
Median: mb = 42.79882248464
Median: mc = 28.78663852368

Inradius: r = 11.75655409332
Circumradius: R = 27.86105476305

Vertex coordinates: A[55.69; 0] B[0; 0] C[24.97219527743; 28.64326530656]
Centroid: CG[26.88773175914; 9.54875510219]
Coordinates of the circumscribed circle: U[27.845; 0.93106391743]
Coordinates of the inscribed circle: I[25.845; 11.75655409332]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.0022383898° = 137°9″ = 0.75504499715 rad
∠ B' = β' = 131.0833381729° = 131°5' = 0.85437560478 rad
∠ C' = γ' = 91.91442343725° = 91°54'51″ = 1.53773866343 rad

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How did we calculate this triangle?

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

p = a+b+c = 38+42+55.69 = 135.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 135.69 }{ 2 } = 67.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 67.85 * (67.85-38)(67.85-42)(67.85-55.69) } ; ; T = sqrt{ 636093.46 } = 797.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 797.55 }{ 38 } = 41.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 797.55 }{ 42 } = 37.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 797.55 }{ 55.69 } = 28.64 ; ;

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{ 42**2+55.69**2-38**2 }{ 2 * 42 * 55.69 } ) = 42° 59'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38**2+55.69**2-42**2 }{ 2 * 38 * 55.69 } ) = 48° 55' ; ; gamma = 180° - alpha - beta = 180° - 42° 59'51" - 48° 55' = 88° 5'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 797.55 }{ 67.85 } = 11.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38 }{ 2 * sin 42° 59'51" } = 27.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 55.69**2 - 38**2 } }{ 2 } = 45.516 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 55.69**2+2 * 38**2 - 42**2 } }{ 2 } = 42.798 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 38**2 - 55.69**2 } }{ 2 } = 28.786 ; ;
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