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 = 163   b = 52   c = 125

Area: T = 2513.742223022
Perimeter: p = 340
Semiperimeter: s = 170

Angle ∠ A = α = 129.3344458296° = 129°20'4″ = 2.25773121335 rad
Angle ∠ B = β = 14.28551411313° = 14°17'7″ = 0.24993227469 rad
Angle ∠ C = γ = 36.38804005731° = 36°22'49″ = 0.63549577732 rad

Height: ha = 30.84334629475
Height: hb = 96.68223934701
Height: hc = 40.22198756835

Median: ma = 50.22220071283
Median: mb = 142.9022064366
Median: mc = 103.5876920024

Inradius: r = 14.78767190013
Circumradius: R = 105.3710788148

Vertex coordinates: A[125; 0] B[0; 0] C[157.96; 40.22198756835]
Centroid: CG[94.32; 13.40766252278]
Coordinates of the circumscribed circle: U[62.5; 84.83436784242]
Coordinates of the inscribed circle: I[118; 14.78767190013]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 50.66655417044° = 50°39'56″ = 2.25773121335 rad
∠ B' = β' = 165.7154858869° = 165°42'53″ = 0.24993227469 rad
∠ C' = γ' = 143.6219599427° = 143°37'11″ = 0.63549577732 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 = 163 ; ; b = 52 ; ; c = 125 ; ;

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

p = a+b+c = 163+52+125 = 340 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 340 }{ 2 } = 170 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 170 * (170-163)(170-52)(170-125) } ; ; T = sqrt{ 6318900 } = 2513.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2513.74 }{ 163 } = 30.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2513.74 }{ 52 } = 96.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2513.74 }{ 125 } = 40.22 ; ;

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{ 163**2-52**2-125**2 }{ 2 * 52 * 125 } ) = 129° 20'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 52**2-163**2-125**2 }{ 2 * 163 * 125 } ) = 14° 17'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 125**2-163**2-52**2 }{ 2 * 52 * 163 } ) = 36° 22'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2513.74 }{ 170 } = 14.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 163 }{ 2 * sin 129° 20'4" } = 105.37 ; ;




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