Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 16.23   b = 17.99   c = 9.3

Area: T = 75.18333559623
Perimeter: p = 43.52
Semiperimeter: s = 21.76

Angle ∠ A = α = 63.9943888827° = 63°59'38″ = 1.11769040612 rad
Angle ∠ B = β = 85.00990690717° = 85°33″ = 1.48436881494 rad
Angle ∠ C = γ = 30.99770421013° = 30°59'49″ = 0.5411000443 rad

Height: ha = 9.2654738874
Height: hb = 8.35883497457
Height: hc = 16.16884636478

Median: ma = 11.79988060837
Median: mb = 9.69774958108
Median: mc = 16.49895118181

Inradius: r = 3.45551174615
Circumradius: R = 9.02992345136

Vertex coordinates: A[9.3; 0] B[0; 0] C[1.41219784946; 16.16884636478]
Centroid: CG[3.57106594982; 5.38994878826]
Coordinates of the circumscribed circle: U[4.65; 7.74398046423]
Coordinates of the inscribed circle: I[3.77; 3.45551174615]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.0066111173° = 116°22″ = 1.11769040612 rad
∠ B' = β' = 94.99109309283° = 94°59'27″ = 1.48436881494 rad
∠ C' = γ' = 149.0032957899° = 149°11″ = 0.5411000443 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 = 16.23+17.99+9.3 = 43.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43.52 }{ 2 } = 21.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.76 * (21.76-16.23)(21.76-17.99)(21.76-9.3) } ; ; T = sqrt{ 5652.54 } = 75.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.18 }{ 16.23 } = 9.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.18 }{ 17.99 } = 8.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.18 }{ 9.3 } = 16.17 ; ;

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{ 17.99**2+9.3**2-16.23**2 }{ 2 * 17.99 * 9.3 } ) = 63° 59'38" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16.23**2+9.3**2-17.99**2 }{ 2 * 16.23 * 9.3 } ) = 85° 33" ; ; gamma = 180° - alpha - beta = 180° - 63° 59'38" - 85° 33" = 30° 59'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.18 }{ 21.76 } = 3.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16.23 }{ 2 * sin 63° 59'38" } = 9.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.99**2+2 * 9.3**2 - 16.23**2 } }{ 2 } = 11.799 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.3**2+2 * 16.23**2 - 17.99**2 } }{ 2 } = 9.697 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.99**2+2 * 16.23**2 - 9.3**2 } }{ 2 } = 16.49 ; ;
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