Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 6.4   b = 8.49   c = 10.05

Area: T = 27.00108099071
Perimeter: p = 24.94
Semiperimeter: s = 12.47

Angle ∠ A = α = 39.26441825973° = 39°15'51″ = 0.68552892644 rad
Angle ∠ B = β = 57.09655233471° = 57°5'44″ = 0.99765048706 rad
Angle ∠ C = γ = 83.64402940556° = 83°38'25″ = 1.46597985186 rad

Height: ha = 8.4387753096
Height: hb = 6.36106148191
Height: hc = 5.37332955039

Median: ma = 8.73550615338
Median: mb = 7.27774463241
Median: mc = 5.59219070987

Inradius: r = 2.165526142
Circumradius: R = 5.05661150006

Vertex coordinates: A[10.05; 0] B[0; 0] C[3.47767363184; 5.37332955039]
Centroid: CG[4.50989121061; 1.79110985013]
Coordinates of the circumscribed circle: U[5.025; 0.56600659777]
Coordinates of the inscribed circle: I[3.98; 2.165526142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.7365817403° = 140°44'9″ = 0.68552892644 rad
∠ B' = β' = 122.9044476653° = 122°54'16″ = 0.99765048706 rad
∠ C' = γ' = 96.36597059444° = 96°21'35″ = 1.46597985186 rad

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How did we calculate this triangle?

a = 6.4 ; ; b = 8.49 ; ; c = 10.05 ; ;

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

p = a+b+c = 6.4+8.49+10.05 = 24.94 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.94 }{ 2 } = 12.47 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.47 * (12.47-6.4)(12.47-8.49)(12.47-10.05) } ; ; T = sqrt{ 729.04 } = 27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27 }{ 6.4 } = 8.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27 }{ 8.49 } = 6.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27 }{ 10.05 } = 5.37 ; ;

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{ 8.49**2+10.05**2-6.4**2 }{ 2 * 8.49 * 10.05 } ) = 39° 15'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.4**2+10.05**2-8.49**2 }{ 2 * 6.4 * 10.05 } ) = 57° 5'44" ; ; gamma = 180° - alpha - beta = 180° - 39° 15'51" - 57° 5'44" = 83° 38'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27 }{ 12.47 } = 2.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.4 }{ 2 * sin 39° 15'51" } = 5.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.49**2+2 * 10.05**2 - 6.4**2 } }{ 2 } = 8.735 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.05**2+2 * 6.4**2 - 8.49**2 } }{ 2 } = 7.277 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.49**2+2 * 6.4**2 - 10.05**2 } }{ 2 } = 5.592 ; ;
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