Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 10.77   b = 5.39   c = 12.04

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

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

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

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

Inradius: r = 2.05985207455
Circumradius: R = 6.02200015532

Vertex coordinates: A[12.04; 0] B[0; 0] C[9.63304983389; 4.82114522444]
Centroid: CG[7.22334994463; 1.60771507481]
Coordinates of the circumscribed circle: U[6.02; 0.00443244232]
Coordinates of the inscribed circle: I[8.71; 2.05985207455]

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

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How did we calculate this triangle?

a = 10.77 ; ; b = 5.39 ; ; c = 12.04 ; ;

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

p = a+b+c = 10.77+5.39+12.04 = 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 * (14.1-10.77)(14.1-5.39)(14.1-12.04) } ; ; 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 }{ 10.77 } = 5.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.03 }{ 5.39 } = 10.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.03 }{ 12.04 } = 4.82 ; ;

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

6. Inradius

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

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.77 }{ 2 * sin 63° 26'48" } = 6.02 ; ;

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