Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 40   b = 60   c = 80

Area: T = 1161.895500386
Perimeter: p = 180
Semiperimeter: s = 90

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 58.09547501931
Height: hb = 38.73298334621
Height: hc = 29.04773750966

Median: ma = 67.82332998313
Median: mb = 55.67876436283
Median: mc = 31.62327766017

Inradius: r = 12.91099444874
Circumradius: R = 41.31218223595

Vertex coordinates: A[80; 0] B[0; 0] C[27.5; 29.04773750966]
Centroid: CG[35.83333333333; 9.68224583655]
Coordinates of the circumscribed circle: U[40; -10.32879555899]
Coordinates of the inscribed circle: I[30; 12.91099444874]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 40 ; ; b = 60 ; ; c = 80 ; ;

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

p = a+b+c = 40+60+80 = 180 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-40)(90-60)(90-80) } ; ; T = sqrt{ 1350000 } = 1161.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1161.9 }{ 40 } = 58.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1161.9 }{ 60 } = 38.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1161.9 }{ 80 } = 29.05 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 40**2-60**2-80**2 }{ 2 * 60 * 80 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60**2-40**2-80**2 }{ 2 * 40 * 80 } ) = 46° 34'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 80**2-40**2-60**2 }{ 2 * 60 * 40 } ) = 104° 28'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1161.9 }{ 90 } = 12.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 28° 57'18" } = 41.31 ; ;




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