Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 154   b = 179   c = 183

Area: T = 12608.71112744
Perimeter: p = 516
Semiperimeter: s = 258

Angle ∠ A = α = 50.33989029005° = 50°20'20″ = 0.87985795975 rad
Angle ∠ B = β = 63.4843521325° = 63°29'1″ = 1.10879964679 rad
Angle ∠ C = γ = 66.17875757745° = 66°10'39″ = 1.15550165883 rad

Height: ha = 163.7499497069
Height: hb = 140.8799455579
Height: hc = 137.8800123217

Median: ma = 163.8176971038
Median: mb = 143.5
Median: mc = 139.6654777235

Inradius: r = 48.87109739316
Circumradius: R = 100.0221681246

Vertex coordinates: A[183; 0] B[0; 0] C[68.75440983607; 137.8800123217]
Centroid: CG[83.91880327869; 45.93333744057]
Coordinates of the circumscribed circle: U[91.5; 40.3999093049]
Coordinates of the inscribed circle: I[79; 48.87109739316]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.6611097099° = 129°39'40″ = 0.87985795975 rad
∠ B' = β' = 116.5166478675° = 116°30'59″ = 1.10879964679 rad
∠ C' = γ' = 113.8222424226° = 113°49'21″ = 1.15550165883 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 = 154 ; ; b = 179 ; ; c = 183 ; ;

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

p = a+b+c = 154+179+183 = 516 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 516 }{ 2 } = 258 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 258 * (258-154)(258-179)(258-183) } ; ; T = sqrt{ 158979600 } = 12608.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12608.71 }{ 154 } = 163.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12608.71 }{ 179 } = 140.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12608.71 }{ 183 } = 137.8 ; ;

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{ 154**2-179**2-183**2 }{ 2 * 179 * 183 } ) = 50° 20'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 179**2-154**2-183**2 }{ 2 * 154 * 183 } ) = 63° 29'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 183**2-154**2-179**2 }{ 2 * 179 * 154 } ) = 66° 10'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12608.71 }{ 258 } = 48.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 154 }{ 2 * sin 50° 20'20" } = 100.02 ; ;




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