Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 17.32   b = 10   c = 20

Area: T = 86.65999998882
Perimeter: p = 47.32
Semiperimeter: s = 23.66

Angle ∠ A = α = 59.99770889407° = 59°59'50″ = 1.04771467436 rad
Angle ∠ B = β = 309.9999999573° = 30° = 0.52435987749 rad
Angle ∠ C = γ = 90.0032911102° = 90°10″ = 1.57108471351 rad

Height: ha = 10.9999999871
Height: hb = 17.32199999776
Height: hc = 8.66599999888

Median: ma = 13.22989228586
Median: mb = 18.02875123076
Median: mc = 10.9995599903

Inradius: r = 3.66601859632
Circumradius: R = 100.0000000129

Vertex coordinates: A[20; 0] B[0; 0] C[154.99956; 8.66599999888]
Centroid: CG[11.667652; 2.88766666629]
Coordinates of the circumscribed circle: U[10; -0.00105080831]
Coordinates of the inscribed circle: I[13.66; 3.66601859632]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.0032911059° = 120°10″ = 1.04771467436 rad
∠ B' = β' = 1500.000000043° = 150° = 0.52435987749 rad
∠ C' = γ' = 89.9977088898° = 89°59'50″ = 1.57108471351 rad

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How did we calculate this triangle?

a = 17.32 ; ; b = 10 ; ; c = 20 ; ;

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

p = a+b+c = 17.32+10+20 = 47.32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47.32 }{ 2 } = 23.66 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.66 * (23.66-17.32)(23.66-10)(23.66-20) } ; ; T = sqrt{ 7499.56 } = 86.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.6 }{ 17.32 } = 10 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.6 }{ 10 } = 17.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.6 }{ 20 } = 8.66 ; ;

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{ 10**2+20**2-17.32**2 }{ 2 * 10 * 20 } ) = 59° 59'50" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17.32**2+20**2-10**2 }{ 2 * 17.32 * 20 } ) = 30° ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 17.32**2+10**2-20**2 }{ 2 * 17.32 * 10 } ) = 90° 10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.6 }{ 23.66 } = 3.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.32 }{ 2 * sin 59° 59'50" } = 10 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 20**2 - 17.32**2 } }{ 2 } = 13.229 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 17.32**2 - 10**2 } }{ 2 } = 18.028 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 17.32**2 - 20**2 } }{ 2 } = 10 ; ;
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