Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 11.4   b = 12.8   c = 10.27

Area: T = 55.73656982808
Perimeter: p = 34.47
Semiperimeter: s = 17.235

Angle ∠ A = α = 57.99220934472° = 57°59'32″ = 1.01221529708 rad
Angle ∠ B = β = 72.19767849441° = 72°11'48″ = 1.26600716066 rad
Angle ∠ C = γ = 49.81111216087° = 49°48'40″ = 0.86993680762 rad

Height: ha = 9.77881926808
Height: hb = 8.70987028564
Height: hc = 10.85440795094

Median: ma = 10.10877420822
Median: mb = 8.76110758472
Median: mc = 10.97986964162

Inradius: r = 3.23438670311
Circumradius: R = 6.72218965861

Vertex coordinates: A[10.27; 0] B[0; 0] C[3.48655355404; 10.85440795094]
Centroid: CG[4.58551785135; 3.61880265031]
Coordinates of the circumscribed circle: U[5.135; 4.33877031612]
Coordinates of the inscribed circle: I[4.435; 3.23438670311]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.0087906553° = 122°28″ = 1.01221529708 rad
∠ B' = β' = 107.8033215056° = 107°48'12″ = 1.26600716066 rad
∠ C' = γ' = 130.1898878391° = 130°11'20″ = 0.86993680762 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 = 11.4+12.8+10.27 = 34.47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34.47 }{ 2 } = 17.24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.24 * (17.24-11.4)(17.24-12.8)(17.24-10.27) } ; ; T = sqrt{ 3106.47 } = 55.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.74 }{ 11.4 } = 9.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.74 }{ 12.8 } = 8.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.74 }{ 10.27 } = 10.85 ; ;

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{ 12.8**2+10.27**2-11.4**2 }{ 2 * 12.8 * 10.27 } ) = 57° 59'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11.4**2+10.27**2-12.8**2 }{ 2 * 11.4 * 10.27 } ) = 72° 11'48" ; ; gamma = 180° - alpha - beta = 180° - 57° 59'32" - 72° 11'48" = 49° 48'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.74 }{ 17.24 } = 3.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11.4 }{ 2 * sin 57° 59'32" } = 6.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.8**2+2 * 10.27**2 - 11.4**2 } }{ 2 } = 10.108 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.27**2+2 * 11.4**2 - 12.8**2 } }{ 2 } = 8.761 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 12.8**2+2 * 11.4**2 - 10.27**2 } }{ 2 } = 10.979 ; ;
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