Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 44   b = 32   c = 60.31

Area: T = 683.3344013904
Perimeter: p = 136.31
Semiperimeter: s = 68.155

Angle ∠ A = α = 45.08443902241° = 45°5'4″ = 0.78768710507 rad
Angle ∠ B = β = 30.99985488767° = 30°59'55″ = 0.54110267412 rad
Angle ∠ C = γ = 103.9177060899° = 103°55'1″ = 1.81436948617 rad

Height: ha = 31.06106369956
Height: hb = 42.7088375869
Height: hc = 22.66107200764

Median: ma = 42.97326430418
Median: mb = 50.30655469109
Median: mc = 23.88988253165

Inradius: r = 10.02661758331
Circumradius: R = 31.06769739367

Vertex coordinates: A[60.31; 0] B[0; 0] C[37.71659351683; 22.66107200764]
Centroid: CG[32.67553117228; 7.55435733588]
Coordinates of the circumscribed circle: U[30.155; -7.47221378857]
Coordinates of the inscribed circle: I[36.155; 10.02661758331]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9165609776° = 134°54'56″ = 0.78768710507 rad
∠ B' = β' = 149.0011451123° = 149°5″ = 0.54110267412 rad
∠ C' = γ' = 76.08329391009° = 76°4'59″ = 1.81436948617 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 = 44+32+60.31 = 136.31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 136.31 }{ 2 } = 68.16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 68.16 * (68.16-44)(68.16-32)(68.16-60.31) } ; ; T = sqrt{ 466945.37 } = 683.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 683.33 }{ 44 } = 31.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 683.33 }{ 32 } = 42.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 683.33 }{ 60.31 } = 22.66 ; ;

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{ 32**2+60.31**2-44**2 }{ 2 * 32 * 60.31 } ) = 45° 5'4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 44**2+60.31**2-32**2 }{ 2 * 44 * 60.31 } ) = 30° 59'55" ; ;
 gamma = 180° - alpha - beta = 180° - 45° 5'4" - 30° 59'55" = 103° 55'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 683.33 }{ 68.16 } = 10.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 44 }{ 2 * sin 45° 5'4" } = 31.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 60.31**2 - 44**2 } }{ 2 } = 42.973 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 60.31**2+2 * 44**2 - 32**2 } }{ 2 } = 50.306 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 44**2 - 60.31**2 } }{ 2 } = 23.889 ; ;
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