Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 792.78   b = 500   c = 400

Area: T = 83762.1988324
Perimeter: p = 1692.78
Semiperimeter: s = 846.39

Angle ∠ A = α = 123.1110147668° = 123°6'37″ = 2.14986774194 rad
Angle ∠ B = β = 31.88994147192° = 31°53'22″ = 0.55765752834 rad
Angle ∠ C = γ = 255.0004376124° = 25°2″ = 0.43663399508 rad

Height: ha = 211.3132591952
Height: hb = 335.0498793296
Height: hc = 418.811099162

Median: ma = 218.8033491517
Median: mb = 575.9777485845
Median: mc = 631.8622377579

Inradius: r = 98.96440689564
Circumradius: R = 473.2332565443

Vertex coordinates: A[400; 0] B[0; 0] C[673.12551605; 418.811099162]
Centroid: CG[357.7088386833; 139.6043663873]
Coordinates of the circumscribed circle: U[200; 428.8932831597]
Coordinates of the inscribed circle: I[346.39; 98.96440689564]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 56.89898523315° = 56°53'23″ = 2.14986774194 rad
∠ B' = β' = 148.1110585281° = 148°6'38″ = 0.55765752834 rad
∠ C' = γ' = 1554.999562388° = 154°59'58″ = 0.43663399508 rad

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How did we calculate this triangle?

a = 792.78 ; ; b = 500 ; ; c = 400 ; ;

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

p = a+b+c = 792.78+500+400 = 1692.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1692.78 }{ 2 } = 846.39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 846.39 * (846.39-792.78)(846.39-500)(846.39-400) } ; ; T = sqrt{ 7016105868.07 } = 83762.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83762.2 }{ 792.78 } = 211.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83762.2 }{ 500 } = 335.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83762.2 }{ 400 } = 418.81 ; ;

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{ 500**2+400**2-792.78**2 }{ 2 * 500 * 400 } ) = 123° 6'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 792.78**2+400**2-500**2 }{ 2 * 792.78 * 400 } ) = 31° 53'22" ; ; gamma = 180° - alpha - beta = 180° - 123° 6'37" - 31° 53'22" = 25° 2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83762.2 }{ 846.39 } = 98.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 792.78 }{ 2 * sin 123° 6'37" } = 473.23 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 500**2+2 * 400**2 - 792.78**2 } }{ 2 } = 218.803 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 400**2+2 * 792.78**2 - 500**2 } }{ 2 } = 575.977 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 500**2+2 * 792.78**2 - 400**2 } }{ 2 } = 631.862 ; ;
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