Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 160   b = 192   c = 106.13

Area: T = 8490.439999934
Perimeter: p = 458.13
Semiperimeter: s = 229.065

Angle ∠ A = α = 56.44326902314° = 56°26'34″ = 0.98551107832 rad
Angle ∠ B = β = 90.00107138016° = 90°3″ = 1.5710808785 rad
Angle ∠ C = γ = 33.5576595967° = 33°33'24″ = 0.58656730854 rad

Height: ha = 106.1329999992
Height: hb = 88.44216666598
Height: hc = 1609.999999988

Median: ma = 132.9055185941
Median: mb = 95.99988981708
Median: mc = 168.5710773787

Inradius: r = 37.06554617656
Circumradius: R = 966.0000000074

Vertex coordinates: A[106.13; 0] B[0; 0] C[-0.00219933101; 1609.999999988]
Centroid: CG[35.376600223; 53.33333333292]
Coordinates of the circumscribed circle: U[53.065; 80.00106611]
Coordinates of the inscribed circle: I[37.065; 37.06554617656]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.5577309769° = 123°33'26″ = 0.98551107832 rad
∠ B' = β' = 89.99992861984° = 89°59'57″ = 1.5710808785 rad
∠ C' = γ' = 146.4433404033° = 146°26'36″ = 0.58656730854 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 = 160+192+106.13 = 458.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 458.13 }{ 2 } = 229.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 229.07 * (229.07-160)(229.07-192)(229.07-106.13) } ; ; T = sqrt{ 72086892.15 } = 8490.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8490.4 }{ 160 } = 106.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8490.4 }{ 192 } = 88.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8490.4 }{ 106.13 } = 160 ; ;

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{ 192**2+106.13**2-160**2 }{ 2 * 192 * 106.13 } ) = 56° 26'34" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 160**2+106.13**2-192**2 }{ 2 * 160 * 106.13 } ) = 90° 3" ; ; gamma = 180° - alpha - beta = 180° - 56° 26'34" - 90° 3" = 33° 33'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8490.4 }{ 229.07 } = 37.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 160 }{ 2 * sin 56° 26'34" } = 96 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 192**2+2 * 106.13**2 - 160**2 } }{ 2 } = 132.905 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 106.13**2+2 * 160**2 - 192**2 } }{ 2 } = 95.999 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 192**2+2 * 160**2 - 106.13**2 } }{ 2 } = 168.571 ; ;
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