Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6.8   b = 5.9   c = 9.67

Area: T = 19.81767123452
Perimeter: p = 22.37
Semiperimeter: s = 11.185

Angle ∠ A = α = 44.0021508735° = 44°5″ = 0.76879712033 rad
Angle ∠ B = β = 37.06660101236° = 37°3'58″ = 0.64769239172 rad
Angle ∠ C = γ = 98.93224811413° = 98°55'57″ = 1.72766975331 rad

Height: ha = 5.82884448074
Height: hb = 6.71875296086
Height: hc = 4.09985961417

Median: ma = 7.25325478282
Median: mb = 7.82112499001
Median: mc = 4.14109872011

Inradius: r = 1.77217221587
Circumradius: R = 4.89443587771

Vertex coordinates: A[9.67; 0] B[0; 0] C[5.42660031024; 4.09985961417]
Centroid: CG[5.03220010341; 1.36661987139]
Coordinates of the circumscribed circle: U[4.835; -0.76599492344]
Coordinates of the inscribed circle: I[5.285; 1.77217221587]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.9988491265° = 135°59'55″ = 0.76879712033 rad
∠ B' = β' = 142.9343989876° = 142°56'2″ = 0.64769239172 rad
∠ C' = γ' = 81.06875188587° = 81°4'3″ = 1.72766975331 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 = 6.8+5.9+9.67 = 22.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.37 }{ 2 } = 11.19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.19 * (11.19-6.8)(11.19-5.9)(11.19-9.67) } ; ; T = sqrt{ 392.7 } = 19.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.82 }{ 6.8 } = 5.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.82 }{ 5.9 } = 6.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.82 }{ 9.67 } = 4.1 ; ;

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{ 5.9**2+9.67**2-6.8**2 }{ 2 * 5.9 * 9.67 } ) = 44° 5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.8**2+9.67**2-5.9**2 }{ 2 * 6.8 * 9.67 } ) = 37° 3'58" ; ; gamma = 180° - alpha - beta = 180° - 44° 5" - 37° 3'58" = 98° 55'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.82 }{ 11.19 } = 1.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6.8 }{ 2 * sin 44° 5" } = 4.89 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.9**2+2 * 9.67**2 - 6.8**2 } }{ 2 } = 7.253 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.67**2+2 * 6.8**2 - 5.9**2 } }{ 2 } = 7.821 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.9**2+2 * 6.8**2 - 9.67**2 } }{ 2 } = 4.141 ; ;
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