Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 9.9   b = 5.39   c = 9.22

Area: T = 24.52217653324
Perimeter: p = 24.51
Semiperimeter: s = 12.255

Angle ∠ A = α = 80.70767539998° = 80°42'24″ = 1.40985985859 rad
Angle ∠ B = β = 32.54999233514° = 32°30' = 0.56772306691 rad
Angle ∠ C = γ = 66.79333226488° = 66°47'36″ = 1.16657633986 rad

Height: ha = 4.95438919864
Height: hb = 9.09989852811
Height: hc = 5.31992549528

Median: ma = 5.70333104422
Median: mb = 9.1798571512
Median: mc = 6.50222265417

Inradius: r = 2.00109600434
Circumradius: R = 5.01658340288

Vertex coordinates: A[9.22; 0] B[0; 0] C[8.35495824295; 5.31992549528]
Centroid: CG[5.85765274765; 1.77330849843]
Coordinates of the circumscribed circle: U[4.61; 1.97664845064]
Coordinates of the inscribed circle: I[6.865; 2.00109600434]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.29332460002° = 99°17'36″ = 1.40985985859 rad
∠ B' = β' = 147.5500076649° = 147°30' = 0.56772306691 rad
∠ C' = γ' = 113.2076677351° = 113°12'24″ = 1.16657633986 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 = 9.9+5.39+9.22 = 24.51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.51 }{ 2 } = 12.26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.26 * (12.26-9.9)(12.26-5.39)(12.26-9.22) } ; ; T = sqrt{ 601.32 } = 24.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.52 }{ 9.9 } = 4.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.52 }{ 5.39 } = 9.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.52 }{ 9.22 } = 5.32 ; ;

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+9.22**2-9.9**2 }{ 2 * 5.39 * 9.22 } ) = 80° 42'24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9.9**2+9.22**2-5.39**2 }{ 2 * 9.9 * 9.22 } ) = 32° 30' ; ; gamma = 180° - alpha - beta = 180° - 80° 42'24" - 32° 30' = 66° 47'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.52 }{ 12.26 } = 2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9.9 }{ 2 * sin 80° 42'24" } = 5.02 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 9.22**2 - 9.9**2 } }{ 2 } = 5.703 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.22**2+2 * 9.9**2 - 5.39**2 } }{ 2 } = 9.179 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 9.9**2 - 9.22**2 } }{ 2 } = 6.502 ; ;
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