136 206 110 triangle

Obtuse scalene triangle.

Sides: a = 136   b = 206   c = 110

Area: T = 6869.411045505
Perimeter: p = 452
Semiperimeter: s = 226

Angle ∠ A = α = 37.32326470536° = 37°19'22″ = 0.65114030766 rad
Angle ∠ B = β = 113.311100629° = 113°18'40″ = 1.97876501385 rad
Angle ∠ C = γ = 29.36663466567° = 29°21'59″ = 0.51325394384 rad

Height: ha = 101.0210741986
Height: hb = 66.69333053889
Height: hc = 124.898837191

Median: ma = 150.4799234448
Median: mb = 68.47662732631
Median: mc = 165.6533252307

Inradius: r = 30.39656214825
Circumradius: R = 112.1555184938

Vertex coordinates: A[110; 0] B[0; 0] C[-53.81881818182; 124.898837191]
Centroid: CG[18.72772727273; 41.63327906367]
Coordinates of the circumscribed circle: U[55; 97.74334678555]
Coordinates of the inscribed circle: I[20; 30.39656214825]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6777352946° = 142°40'38″ = 0.65114030766 rad
∠ B' = β' = 66.68989937103° = 66°41'20″ = 1.97876501385 rad
∠ C' = γ' = 150.6343653343° = 150°38'1″ = 0.51325394384 rad

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How did we calculate this triangle?

a = 136 ; ; b = 206 ; ; c = 110 ; ;

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

p = a+b+c = 136+206+110 = 452 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 452 }{ 2 } = 226 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 226 * (226-136)(226-206)(226-110) } ; ; T = sqrt{ 47188800 } = 6869.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6869.41 }{ 136 } = 101.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6869.41 }{ 206 } = 66.69 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6869.41 }{ 110 } = 124.9 ; ;

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{ 136**2-206**2-110**2 }{ 2 * 206 * 110 } ) = 37° 19'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 206**2-136**2-110**2 }{ 2 * 136 * 110 } ) = 113° 18'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 110**2-136**2-206**2 }{ 2 * 206 * 136 } ) = 29° 21'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6869.41 }{ 226 } = 30.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 136 }{ 2 * sin 37° 19'22" } = 112.16 ; ;




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