Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 335.41   b = 100   c = 350

Area: T = 16770.5
Perimeter: p = 785.41
Semiperimeter: s = 392.705

Angle ∠ A = α = 73.39883377432° = 73°23'54″ = 1.28110426591 rad
Angle ∠ B = β = 16.6021549599° = 16°36'6″ = 0.29897517014 rad
Angle ∠ C = γ = 900.0001126578° = 90° = 1.5710798293 rad

Height: ha = 100.9999999998
Height: hb = 335.4109999999
Height: hc = 95.83114285712

Median: ma = 195.2566326338
Median: mb = 339.1166401918
Median: mc = 1754.999811571

Inradius: r = 42.70550839688
Circumradius: R = 175

Vertex coordinates: A[350; 0] B[0; 0] C[321.4288383; 95.83114285712]
Centroid: CG[223.8099461; 31.94438095237]
Coordinates of the circumscribed circle: U[175; -00.0003440938]
Coordinates of the inscribed circle: I[292.705; 42.70550839688]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 106.6021662257° = 106°36'6″ = 1.28110426591 rad
∠ B' = β' = 163.3988450401° = 163°23'54″ = 0.29897517014 rad
∠ C' = γ' = 909.9998873422° = 90° = 1.5710798293 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 = 335.41+100+350 = 785.41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 785.41 }{ 2 } = 392.71 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 392.71 * (392.71-335.41)(392.71-100)(392.71-350) } ; ; T = sqrt{ 281249670.25 } = 16770.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16770.5 }{ 335.41 } = 100 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16770.5 }{ 100 } = 335.41 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16770.5 }{ 350 } = 95.83 ; ;

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{ 100**2+350**2-335.41**2 }{ 2 * 100 * 350 } ) = 73° 23'54" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 335.41**2+350**2-100**2 }{ 2 * 335.41 * 350 } ) = 16° 36'6" ; ; gamma = 180° - alpha - beta = 180° - 73° 23'54" - 16° 36'6" = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16770.5 }{ 392.71 } = 42.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 335.41 }{ 2 * sin 73° 23'54" } = 175 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 350**2 - 335.41**2 } }{ 2 } = 195.256 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 350**2+2 * 335.41**2 - 100**2 } }{ 2 } = 339.116 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 335.41**2 - 350**2 } }{ 2 } = 175 ; ;
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