Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 6.4   b = 5.39   c = 3.74

Area: T = 10.06658813069
Perimeter: p = 15.53
Semiperimeter: s = 7.765

Angle ∠ A = α = 87.04331741374° = 87°2'35″ = 1.51991899801 rad
Angle ∠ B = β = 57.25328886245° = 57°15'10″ = 0.99992514128 rad
Angle ∠ C = γ = 35.70439372381° = 35°42'14″ = 0.62331512607 rad

Height: ha = 3.14655879084
Height: hb = 3.73550208931
Height: hc = 5.38328242283

Median: ma = 3.35985487938
Median: mb = 4.49656395541
Median: mc = 5.61333011678

Inradius: r = 1.29663143988
Circumradius: R = 3.20442658776

Vertex coordinates: A[3.74; 0] B[0; 0] C[3.46219652406; 5.38328242283]
Centroid: CG[2.40106550802; 1.79442747428]
Coordinates of the circumscribed circle: U[1.87; 2.60220030389]
Coordinates of the inscribed circle: I[2.375; 1.29663143988]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 92.95768258626° = 92°57'25″ = 1.51991899801 rad
∠ B' = β' = 122.7477111375° = 122°44'50″ = 0.99992514128 rad
∠ C' = γ' = 144.2966062762° = 144°17'46″ = 0.62331512607 rad

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How did we calculate this triangle?

a = 6.4 ; ; b = 5.39 ; ; c = 3.74 ; ;

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

p = a+b+c = 6.4+5.39+3.74 = 15.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.53 }{ 2 } = 7.77 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.77 * (7.77-6.4)(7.77-5.39)(7.77-3.74) } ; ; T = sqrt{ 101.32 } = 10.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.07 }{ 6.4 } = 3.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.07 }{ 5.39 } = 3.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.07 }{ 3.74 } = 5.38 ; ;

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{ 5.39**2+3.74**2-6.4**2 }{ 2 * 5.39 * 3.74 } ) = 87° 2'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.4**2+3.74**2-5.39**2 }{ 2 * 6.4 * 3.74 } ) = 57° 15'10" ; ; gamma = 180° - alpha - beta = 180° - 87° 2'35" - 57° 15'10" = 35° 42'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.07 }{ 7.77 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.4 }{ 2 * sin 87° 2'35" } = 3.2 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 3.74**2 - 6.4**2 } }{ 2 } = 3.359 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.74**2+2 * 6.4**2 - 5.39**2 } }{ 2 } = 4.496 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 6.4**2 - 3.74**2 } }{ 2 } = 5.613 ; ;
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