Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 20   b = 24   c = 29

Area: T = 237.6155103687
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 43.06329928689° = 43°3'47″ = 0.75215910113 rad
Angle ∠ B = β = 55.02110210382° = 55°1'16″ = 0.96602979749 rad
Angle ∠ C = γ = 81.91659860929° = 81°54'58″ = 1.43297036673 rad

Height: ha = 23.76215103687
Height: hb = 19.80112586406
Height: hc = 16.38772485301

Median: ma = 24.66877927671
Median: mb = 21.82988799529
Median: mc = 16.66658333125

Inradius: r = 6.51100028407
Circumradius: R = 14.64655336635

Vertex coordinates: A[29; 0] B[0; 0] C[11.46655172414; 16.38772485301]
Centroid: CG[13.48985057471; 5.46224161767]
Coordinates of the circumscribed circle: U[14.5; 2.06595281714]
Coordinates of the inscribed circle: I[12.5; 6.51100028407]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.9377007131° = 136°56'13″ = 0.75215910113 rad
∠ B' = β' = 124.9798978962° = 124°58'44″ = 0.96602979749 rad
∠ C' = γ' = 98.08440139071° = 98°5'2″ = 1.43297036673 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 = 20+24+29 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-20)(36.5-24)(36.5-29) } ; ; T = sqrt{ 56460.94 } = 237.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 237.62 }{ 20 } = 23.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 237.62 }{ 24 } = 19.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 237.62 }{ 29 } = 16.39 ; ;

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{ 24**2+29**2-20**2 }{ 2 * 24 * 29 } ) = 43° 3'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 20**2+29**2-24**2 }{ 2 * 20 * 29 } ) = 55° 1'16" ; ; gamma = 180° - alpha - beta = 180° - 43° 3'47" - 55° 1'16" = 81° 54'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 237.62 }{ 36.5 } = 6.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 20 }{ 2 * sin 43° 3'47" } = 14.65 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 29**2 - 20**2 } }{ 2 } = 24.668 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 20**2 - 24**2 } }{ 2 } = 21.829 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 20**2 - 29**2 } }{ 2 } = 16.666 ; ;
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