Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 7.07   b = 5.66   c = 4.24

Area: T = 11.99991979142
Perimeter: p = 16.97
Semiperimeter: s = 8.485

Angle ∠ A = α = 89.96662171092° = 89°57'58″ = 1.57702067041 rad
Angle ∠ B = β = 53.18441502004° = 53°11'3″ = 0.92882385309 rad
Angle ∠ C = γ = 36.85496326904° = 36°50'59″ = 0.64331474186 rad

Height: ha = 3.39443982784
Height: hb = 4.2439999263
Height: hc = 5.66599990161

Median: ma = 3.53770008482
Median: mb = 5.09663074868
Median: mc = 6.04328345998

Inradius: r = 1.41441659298
Circumradius: R = 3.53550006145

Vertex coordinates: A[4.24; 0] B[0; 0] C[4.23766627358; 5.66599990161]
Centroid: CG[2.82655542453; 1.88766663387]
Coordinates of the circumscribed circle: U[2.12; 2.82987504917]
Coordinates of the inscribed circle: I[2.825; 1.41441659298]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.03437828908° = 90°2'2″ = 1.57702067041 rad
∠ B' = β' = 126.81658498° = 126°48'57″ = 0.92882385309 rad
∠ C' = γ' = 143.155036731° = 143°9'1″ = 0.64331474186 rad

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How did we calculate this triangle?

a = 7.07 ; ; b = 5.66 ; ; c = 4.24 ; ;

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

p = a+b+c = 7.07+5.66+4.24 = 16.97 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.97 }{ 2 } = 8.49 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.49 * (8.49-7.07)(8.49-5.66)(8.49-4.24) } ; ; T = sqrt{ 143.98 } = 12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12 }{ 7.07 } = 3.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12 }{ 5.66 } = 4.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12 }{ 4.24 } = 5.66 ; ;

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{ 5.66**2+4.24**2-7.07**2 }{ 2 * 5.66 * 4.24 } ) = 89° 57'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.07**2+4.24**2-5.66**2 }{ 2 * 7.07 * 4.24 } ) = 53° 11'3" ; ; gamma = 180° - alpha - beta = 180° - 89° 57'58" - 53° 11'3" = 36° 50'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12 }{ 8.49 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.07 }{ 2 * sin 89° 57'58" } = 3.54 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 4.24**2 - 7.07**2 } }{ 2 } = 3.537 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.24**2+2 * 7.07**2 - 5.66**2 } }{ 2 } = 5.096 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.66**2+2 * 7.07**2 - 4.24**2 } }{ 2 } = 6.043 ; ;
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