Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 3370.16   b = 4472.36   c = 5600

Area: T = 7536284.38988
Perimeter: p = 13442.52
Semiperimeter: s = 6721.26

Angle ∠ A = α = 376.9999470947° = 37° = 0.64657708999 rad
Angle ∠ B = β = 533.0000194445° = 53° = 0.92550248429 rad
Angle ∠ C = γ = 900.0000334608° = 90° = 1.57107969108 rad

Height: ha = 4472.36
Height: hb = 3370.16
Height: hc = 2691.533013886

Median: ma = 4779.279896009
Median: mb = 4044.563279719
Median: mc = 2799.998842814

Inradius: r = 1121.261065482
Circumradius: R = 2800

Vertex coordinates: A[5600; 0] B[0; 0] C[2028.2122005; 2691.533013886]
Centroid: CG[2542.7377335; 897.1776712952]
Coordinates of the circumscribed circle: U[2800; -0.00216352037]
Coordinates of the inscribed circle: I[2248.9; 1121.261065482]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1433.000052905° = 143° = 0.64657708999 rad
∠ B' = β' = 1276.999980555° = 127° = 0.92550248429 rad
∠ C' = γ' = 909.9999665392° = 90° = 1.57107969108 rad

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How did we calculate this triangle?

a = 3370.16 ; ; b = 4472.36 ; ; c = 5600 ; ;

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

p = a+b+c = 3370.16+4472.36+5600 = 13442.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 13442.52 }{ 2 } = 6721.26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6721.26 * (6721.26-3370.16)(6721.26-4472.36)(6721.26-5600) } ; ; T = sqrt{ 5.68 * 10**{ 13 } } = 7536284.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7536284.39 }{ 3370.16 } = 4472.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7536284.39 }{ 4472.36 } = 3370.16 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7536284.39 }{ 5600 } = 2691.53 ; ;

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{ 4472.36**2+5600**2-3370.16**2 }{ 2 * 4472.36 * 5600 } ) = 37° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3370.16**2+5600**2-4472.36**2 }{ 2 * 3370.16 * 5600 } ) = 53° ; ; gamma = 180° - alpha - beta = 180° - 37° - 53° = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7536284.39 }{ 6721.26 } = 1121.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3370.16 }{ 2 * sin 37° } = 2800 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4472.36**2+2 * 5600**2 - 3370.16**2 } }{ 2 } = 4779.279 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5600**2+2 * 3370.16**2 - 4472.36**2 } }{ 2 } = 4044.563 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4472.36**2+2 * 3370.16**2 - 5600**2 } }{ 2 } = 2799.998 ; ;
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