Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Obtuse isosceles triangle.

Sides: a = 80   b = 80   c = 120

Area: T = 3174.902157328
Perimeter: p = 280
Semiperimeter: s = 140

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 79.37325393319
Height: hb = 79.37325393319
Height: hc = 52.91550262213

Median: ma = 93.80883151965
Median: mb = 93.80883151965
Median: mc = 52.91550262213

Inradius: r = 22.67878683806
Circumradius: R = 60.47443156815

Vertex coordinates: A[120; 0] B[0; 0] C[60; 52.91550262213]
Centroid: CG[60; 17.63883420738]
Coordinates of the circumscribed circle: U[60; -7.55992894602]
Coordinates of the inscribed circle: I[60; 22.67878683806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 80 ; ; b = 80 ; ; c = 120 ; ;

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

p = a+b+c = 80+80+120 = 280 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 280 }{ 2 } = 140 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 140 * (140-80)(140-80)(140-120) } ; ; T = sqrt{ 10080000 } = 3174.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3174.9 }{ 80 } = 79.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3174.9 }{ 80 } = 79.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3174.9 }{ 120 } = 52.92 ; ;

6. 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{ 80**2+120**2-80**2 }{ 2 * 80 * 120 } ) = 41° 24'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 80**2+120**2-80**2 }{ 2 * 80 * 120 } ) = 41° 24'35" ; ;
 gamma = 180° - alpha - beta = 180° - 41° 24'35" - 41° 24'35" = 97° 10'51" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3174.9 }{ 140 } = 22.68 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 80 }{ 2 * sin 41° 24'35" } = 60.47 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 120**2 - 80**2 } }{ 2 } = 93.808 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 120**2+2 * 80**2 - 80**2 } }{ 2 } = 93.808 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 80**2 - 120**2 } }{ 2 } = 52.915 ; ;
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