Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 12.04   b = 5.39   c = 10.77

Area: T = 29.02551425113
Perimeter: p = 28.2
Semiperimeter: s = 14.1

Angle ∠ A = α = 89.95988420006° = 89°57'32″ = 1.57700779842 rad
Angle ∠ B = β = 26.5954567277° = 26°35'40″ = 0.46441627621 rad
Angle ∠ C = γ = 63.44765907224° = 63°26'48″ = 1.10773519073 rad

Height: ha = 4.82114522444
Height: hb = 10.77699972213
Height: hc = 5.39899986093

Median: ma = 6.02334624594
Median: mb = 11.11001903137
Median: mc = 7.61663393438

Inradius: r = 2.05985207455
Circumradius: R = 6.02200015532

Vertex coordinates: A[10.77; 0] B[0; 0] C[10.76661281337; 5.39899986093]
Centroid: CG[7.17987093779; 1.79766662031]
Coordinates of the circumscribed circle: U[5.385; 2.69111324198]
Coordinates of the inscribed circle: I[8.71; 2.05985207455]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.04111579994° = 90°2'28″ = 1.57700779842 rad
∠ B' = β' = 153.4055432723° = 153°24'20″ = 0.46441627621 rad
∠ C' = γ' = 116.5533409278° = 116°33'12″ = 1.10773519073 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 = 12.04+5.39+10.77 = 28.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28.2 }{ 2 } = 14.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.1 * (14.1-12.04)(14.1-5.39)(14.1-10.77) } ; ; T = sqrt{ 842.46 } = 29.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.03 }{ 12.04 } = 4.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.03 }{ 5.39 } = 10.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.03 }{ 10.77 } = 5.39 ; ;

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+10.77**2-12.04**2 }{ 2 * 5.39 * 10.77 } ) = 89° 57'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.04**2+10.77**2-5.39**2 }{ 2 * 12.04 * 10.77 } ) = 26° 35'40" ; ; gamma = 180° - alpha - beta = 180° - 89° 57'32" - 26° 35'40" = 63° 26'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.03 }{ 14.1 } = 2.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.04 }{ 2 * sin 89° 57'32" } = 6.02 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 10.77**2 - 12.04**2 } }{ 2 } = 6.023 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.77**2+2 * 12.04**2 - 5.39**2 } }{ 2 } = 11.1 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 12.04**2 - 10.77**2 } }{ 2 } = 7.616 ; ;
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