Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 49   b = 52   c = 17.41

Area: T = 426.5454999144
Perimeter: p = 118.41
Semiperimeter: s = 59.205

Angle ∠ A = α = 70.44327859409° = 70°26'34″ = 1.22994585489 rad
Angle ∠ B = β = 89.99663698591° = 89°59'47″ = 1.57107329689 rad
Angle ∠ C = γ = 19.56108442° = 19°33'39″ = 0.34114011358 rad

Height: ha = 17.41099999651
Height: hb = 16.40655768901
Height: hc = 498.9999999017

Median: ma = 30.05550170521
Median: mb = 26.00110394023
Median: mc = 49.76766853929

Inradius: r = 7.20545435207
Circumradius: R = 266.0000000522

Vertex coordinates: A[17.41; 0] B[0; 0] C[0.00331045376; 498.9999999017]
Centroid: CG[5.80443681792; 16.33333333006]
Coordinates of the circumscribed circle: U[8.705; 24.49994485186]
Coordinates of the inscribed circle: I[7.205; 7.20545435207]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 109.5577214059° = 109°33'26″ = 1.22994585489 rad
∠ B' = β' = 90.00436301409° = 90°13″ = 1.57107329689 rad
∠ C' = γ' = 160.43991558° = 160°26'21″ = 0.34114011358 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 = 49+52+17.41 = 118.41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 118.41 }{ 2 } = 59.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 59.21 * (59.21-49)(59.21-52)(59.21-17.41) } ; ; T = sqrt{ 181940.64 } = 426.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 426.54 }{ 49 } = 17.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 426.54 }{ 52 } = 16.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 426.54 }{ 17.41 } = 49 ; ;

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{ 52**2+17.41**2-49**2 }{ 2 * 52 * 17.41 } ) = 70° 26'34" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 49**2+17.41**2-52**2 }{ 2 * 49 * 17.41 } ) = 89° 59'47" ; ; gamma = 180° - alpha - beta = 180° - 70° 26'34" - 89° 59'47" = 19° 33'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 426.54 }{ 59.21 } = 7.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 49 }{ 2 * sin 70° 26'34" } = 26 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 52**2+2 * 17.41**2 - 49**2 } }{ 2 } = 30.055 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.41**2+2 * 49**2 - 52**2 } }{ 2 } = 26.001 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 52**2+2 * 49**2 - 17.41**2 } }{ 2 } = 49.767 ; ;
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