Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 9.06   b = 13.45   c = 10.05

Area: T = 45.52332269884
Perimeter: p = 32.56
Semiperimeter: s = 16.28

Angle ∠ A = α = 42.34222333441° = 42°20'32″ = 0.73990113845 rad
Angle ∠ B = β = 89.31329602407° = 89°18'47″ = 1.55988052209 rad
Angle ∠ C = γ = 48.34548064152° = 48°20'41″ = 0.84437760482 rad

Height: ha = 10.04992774809
Height: hb = 6.76992530838
Height: hc = 9.05993486544

Median: ma = 10.97441332232
Median: mb = 6.80656906336
Median: mc = 10.3077396616

Inradius: r = 2.7966267014
Circumradius: R = 6.72554835115

Vertex coordinates: A[10.05; 0] B[0; 0] C[0.10986368159; 9.05993486544]
Centroid: CG[3.3866212272; 3.02197828848]
Coordinates of the circumscribed circle: U[5.025; 4.4770067501]
Coordinates of the inscribed circle: I[2.83; 2.7966267014]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.6587766656° = 137°39'28″ = 0.73990113845 rad
∠ B' = β' = 90.68770397593° = 90°41'13″ = 1.55988052209 rad
∠ C' = γ' = 131.6555193585° = 131°39'19″ = 0.84437760482 rad

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How did we calculate this triangle?

a = 9.06 ; ; b = 13.45 ; ; c = 10.05 ; ;

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

p = a+b+c = 9.06+13.45+10.05 = 32.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.56 }{ 2 } = 16.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.28 * (16.28-9.06)(16.28-13.45)(16.28-10.05) } ; ; T = sqrt{ 2072.36 } = 45.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.52 }{ 9.06 } = 10.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.52 }{ 13.45 } = 6.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.52 }{ 10.05 } = 9.06 ; ;

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{ 13.45**2+10.05**2-9.06**2 }{ 2 * 13.45 * 10.05 } ) = 42° 20'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9.06**2+10.05**2-13.45**2 }{ 2 * 9.06 * 10.05 } ) = 89° 18'47" ; ; gamma = 180° - alpha - beta = 180° - 42° 20'32" - 89° 18'47" = 48° 20'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.52 }{ 16.28 } = 2.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9.06 }{ 2 * sin 42° 20'32" } = 6.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.45**2+2 * 10.05**2 - 9.06**2 } }{ 2 } = 10.974 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.05**2+2 * 9.06**2 - 13.45**2 } }{ 2 } = 6.806 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.45**2+2 * 9.06**2 - 10.05**2 } }{ 2 } = 10.307 ; ;
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