Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.61   b = 4.12   c = 3.16

Area: T = 5.55000674777
Perimeter: p = 10.89
Semiperimeter: s = 5.445

Angle ∠ A = α = 57.66329746752° = 57°39'47″ = 1.00664087646 rad
Angle ∠ B = β = 74.64401519127° = 74°38'25″ = 1.30327164051 rad
Angle ∠ C = γ = 47.6976873412° = 47°41'49″ = 0.83224674839 rad

Height: ha = 3.04771287965
Height: hb = 2.67699356688
Height: hc = 3.48110553656

Median: ma = 3.19771823533
Median: mb = 2.69554127699
Median: mc = 3.53765025095

Inradius: r = 1.01101134027
Circumradius: R = 2.1366306154

Vertex coordinates: A[3.16; 0] B[0; 0] C[0.95662183544; 3.48110553656]
Centroid: CG[1.37220727848; 1.16603517885]
Coordinates of the circumscribed circle: U[1.58; 1.43878469959]
Coordinates of the inscribed circle: I[1.325; 1.01101134027]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.3377025325° = 122°20'13″ = 1.00664087646 rad
∠ B' = β' = 105.3659848087° = 105°21'35″ = 1.30327164051 rad
∠ C' = γ' = 132.3033126588° = 132°18'11″ = 0.83224674839 rad

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How did we calculate this triangle?

a = 3.61 ; ; b = 4.12 ; ; c = 3.16 ; ;

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

p = a+b+c = 3.61+4.12+3.16 = 10.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10.89 }{ 2 } = 5.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.45 * (5.45-3.61)(5.45-4.12)(5.45-3.16) } ; ; T = sqrt{ 30.25 } = 5.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.5 }{ 3.61 } = 3.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.5 }{ 4.12 } = 2.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.5 }{ 3.16 } = 3.48 ; ;

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{ 4.12**2+3.16**2-3.61**2 }{ 2 * 4.12 * 3.16 } ) = 57° 39'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.61**2+3.16**2-4.12**2 }{ 2 * 3.61 * 3.16 } ) = 74° 38'25" ; ; gamma = 180° - alpha - beta = 180° - 57° 39'47" - 74° 38'25" = 47° 41'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.5 }{ 5.45 } = 1.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.61 }{ 2 * sin 57° 39'47" } = 2.14 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.12**2+2 * 3.16**2 - 3.61**2 } }{ 2 } = 3.197 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.16**2+2 * 3.61**2 - 4.12**2 } }{ 2 } = 2.695 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.12**2+2 * 3.61**2 - 3.16**2 } }{ 2 } = 3.537 ; ;
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