194 252 180 triangle

Acute scalene triangle.

Sides: a = 194   b = 252   c = 180

Area: T = 17383.4676599
Perimeter: p = 626
Semiperimeter: s = 313

Angle ∠ A = α = 50.03876604588° = 50°2'16″ = 0.8733321925 rad
Angle ∠ B = β = 84.63333931145° = 84°38' = 1.4777131367 rad
Angle ∠ C = γ = 45.32989464266° = 45°19'44″ = 0.79111393616 rad

Height: ha = 179.2110995866
Height: hb = 137.9644020627
Height: hc = 193.1549628878

Median: ma = 196.3243712271
Median: mb = 138.3554616837
Median: mc = 206.0832507749

Inradius: r = 55.53882319458
Circumradius: R = 126.5554734492

Vertex coordinates: A[180; 0] B[0; 0] C[18.14444444444; 193.1549628878]
Centroid: CG[66.04881481481; 64.38332096261]
Coordinates of the circumscribed circle: U[90; 88.97224722735]
Coordinates of the inscribed circle: I[61; 55.53882319458]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.9622339541° = 129°57'44″ = 0.8733321925 rad
∠ B' = β' = 95.36766068855° = 95°22' = 1.4777131367 rad
∠ C' = γ' = 134.6711053573° = 134°40'16″ = 0.79111393616 rad

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How did we calculate this triangle?

a = 194 ; ; b = 252 ; ; c = 180 ; ;

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

p = a+b+c = 194+252+180 = 626 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 626 }{ 2 } = 313 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 313 * (313-194)(313-252)(313-180) } ; ; T = sqrt{ 302184911 } = 17383.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17383.47 }{ 194 } = 179.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17383.47 }{ 252 } = 137.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17383.47 }{ 180 } = 193.15 ; ;

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{ 194**2-252**2-180**2 }{ 2 * 252 * 180 } ) = 50° 2'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 252**2-194**2-180**2 }{ 2 * 194 * 180 } ) = 84° 38' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 180**2-194**2-252**2 }{ 2 * 252 * 194 } ) = 45° 19'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17383.47 }{ 313 } = 55.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 194 }{ 2 * sin 50° 2'16" } = 126.55 ; ;




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