Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 75.73   b = 124   c = 164

Area: T = 4466.973338204
Perimeter: p = 363.73
Semiperimeter: s = 181.865

Angle ∠ A = α = 26.06602994171° = 26°3'37″ = 0.45548380289 rad
Angle ∠ B = β = 465.999653728° = 45°59'59″ = 0.80328454123 rad
Angle ∠ C = γ = 107.9440046855° = 107°56'24″ = 1.88439092124 rad

Height: ha = 117.9711038744
Height: hb = 72.04879577748
Height: hc = 54.47552851468

Median: ma = 140.3654674242
Median: mb = 111.6765943918
Median: mc = 61.89992443411

Inradius: r = 24.56220288788
Circumradius: R = 86.19106456725

Vertex coordinates: A[164; 0] B[0; 0] C[52.6076807622; 54.47552851468]
Centroid: CG[72.20222692073; 18.15884283823]
Coordinates of the circumscribed circle: U[82; -26.5498585677]
Coordinates of the inscribed circle: I[57.865; 24.56220288788]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.9439700583° = 153°56'23″ = 0.45548380289 rad
∠ B' = β' = 1344.000346272° = 134°1″ = 0.80328454123 rad
∠ C' = γ' = 72.0659953145° = 72°3'36″ = 1.88439092124 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 = 75.73+124+164 = 363.73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 363.73 }{ 2 } = 181.87 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 181.87 * (181.87-75.73)(181.87-124)(181.87-164) } ; ; T = sqrt{ 19953851.2 } = 4466.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4466.97 }{ 75.73 } = 117.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4466.97 }{ 124 } = 72.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4466.97 }{ 164 } = 54.48 ; ;

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{ 124**2+164**2-75.73**2 }{ 2 * 124 * 164 } ) = 26° 3'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 75.73**2+164**2-124**2 }{ 2 * 75.73 * 164 } ) = 45° 59'59" ; ; gamma = 180° - alpha - beta = 180° - 26° 3'37" - 45° 59'59" = 107° 56'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4466.97 }{ 181.87 } = 24.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 75.73 }{ 2 * sin 26° 3'37" } = 86.19 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 124**2+2 * 164**2 - 75.73**2 } }{ 2 } = 140.365 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 164**2+2 * 75.73**2 - 124**2 } }{ 2 } = 111.676 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 124**2+2 * 75.73**2 - 164**2 } }{ 2 } = 61.899 ; ;
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