Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 62   b = 54   c = 83.93

Area: T = 1672.4911047
Perimeter: p = 199.93
Semiperimeter: s = 99.965

Angle ∠ A = α = 47.56551407345° = 47°33'55″ = 0.8330168315 rad
Angle ∠ B = β = 40.00219249281° = 40°7″ = 0.69881652971 rad
Angle ∠ C = γ = 92.43329343375° = 92°25'59″ = 1.61332590415 rad

Height: ha = 53.95113240968
Height: hb = 61.94441128519
Height: hc = 39.85444274277

Median: ma = 63.39765491963
Median: mb = 68.66767492313
Median: mc = 40.23660382617

Inradius: r = 16.73107662382
Circumradius: R = 42.00328616153

Vertex coordinates: A[83.93; 0] B[0; 0] C[47.49334165376; 39.85444274277]
Centroid: CG[43.80878055125; 13.28548091426]
Coordinates of the circumscribed circle: U[41.965; -1.78330195937]
Coordinates of the inscribed circle: I[45.965; 16.73107662382]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.4354859266° = 132°26'5″ = 0.8330168315 rad
∠ B' = β' = 139.9988075072° = 139°59'53″ = 0.69881652971 rad
∠ C' = γ' = 87.56770656625° = 87°34'1″ = 1.61332590415 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 = 62+54+83.93 = 199.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 199.93 }{ 2 } = 99.97 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 99.97 * (99.97-62)(99.97-54)(99.97-83.93) } ; ; T = sqrt{ 2797226.3 } = 1672.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1672.49 }{ 62 } = 53.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1672.49 }{ 54 } = 61.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1672.49 }{ 83.93 } = 39.85 ; ;

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{ 54**2+83.93**2-62**2 }{ 2 * 54 * 83.93 } ) = 47° 33'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 62**2+83.93**2-54**2 }{ 2 * 62 * 83.93 } ) = 40° 7" ; ; gamma = 180° - alpha - beta = 180° - 47° 33'55" - 40° 7" = 92° 25'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1672.49 }{ 99.97 } = 16.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 62 }{ 2 * sin 47° 33'55" } = 42 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 54**2+2 * 83.93**2 - 62**2 } }{ 2 } = 63.397 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 83.93**2+2 * 62**2 - 54**2 } }{ 2 } = 68.667 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 54**2+2 * 62**2 - 83.93**2 } }{ 2 } = 40.236 ; ;
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