Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 2.83   b = 6.32   c = 5.66

Area: T = 8.00988593248
Perimeter: p = 14.81
Semiperimeter: s = 7.405

Angle ∠ A = α = 26.60215025216° = 26°36'5″ = 0.4644283805 rad
Angle ∠ B = β = 89.81773934937° = 89°49'3″ = 1.5687609242 rad
Angle ∠ C = γ = 63.58111039847° = 63°34'52″ = 1.11096996066 rad

Height: ha = 5.66599712543
Height: hb = 2.53444491534
Height: hc = 2.83299856271

Median: ma = 5.83298177502
Median: mb = 3.16880672341
Median: mc = 3.99658415885

Inradius: r = 1.08215475118
Circumradius: R = 3.16600160489

Vertex coordinates: A[5.66; 0] B[0; 0] C[0.00990194346; 2.83299856271]
Centroid: CG[1.89896731449; 0.94333285424]
Coordinates of the circumscribed circle: U[2.83; 1.4065987706]
Coordinates of the inscribed circle: I[1.085; 1.08215475118]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.3988497478° = 153°23'55″ = 0.4644283805 rad
∠ B' = β' = 90.18326065063° = 90°10'57″ = 1.5687609242 rad
∠ C' = γ' = 116.4198896015° = 116°25'8″ = 1.11096996066 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 = 2.83+6.32+5.66 = 14.81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14.81 }{ 2 } = 7.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.41 * (7.41-2.83)(7.41-6.32)(7.41-5.66) } ; ; T = sqrt{ 64.14 } = 8.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.01 }{ 2.83 } = 5.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.01 }{ 6.32 } = 2.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.01 }{ 5.66 } = 2.83 ; ;

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{ 6.32**2+5.66**2-2.83**2 }{ 2 * 6.32 * 5.66 } ) = 26° 36'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.83**2+5.66**2-6.32**2 }{ 2 * 2.83 * 5.66 } ) = 89° 49'3" ; ; gamma = 180° - alpha - beta = 180° - 26° 36'5" - 89° 49'3" = 63° 34'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.01 }{ 7.41 } = 1.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.83 }{ 2 * sin 26° 36'5" } = 3.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 5.66**2 - 2.83**2 } }{ 2 } = 5.83 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 2.83**2 - 6.32**2 } }{ 2 } = 3.168 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 2.83**2 - 5.66**2 } }{ 2 } = 3.996 ; ;
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