155 175 260 triangle

Obtuse scalene triangle.

Sides: a = 155   b = 175   c = 260

Area: T = 13170.42114056
Perimeter: p = 590
Semiperimeter: s = 295

Angle ∠ A = α = 35.37545904472° = 35°22'29″ = 0.61774030748 rad
Angle ∠ B = β = 40.81550125579° = 40°48'54″ = 0.71223563534 rad
Angle ∠ C = γ = 103.8110396995° = 103°48'37″ = 1.81218332254 rad

Height: ha = 169.9410921362
Height: hb = 150.5199101778
Height: hc = 101.3110933889

Median: ma = 207.622044697
Median: mb = 195.3366248556
Median: mc = 102.1032889283

Inradius: r = 44.645549629
Circumradius: R = 133.877005212

Vertex coordinates: A[260; 0] B[0; 0] C[117.3087692308; 101.3110933889]
Centroid: CG[125.7699230769; 33.77703112963]
Coordinates of the circumscribed circle: U[130; -31.95660769576]
Coordinates of the inscribed circle: I[120; 44.645549629]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.6255409553° = 144°37'31″ = 0.61774030748 rad
∠ B' = β' = 139.1854987442° = 139°11'6″ = 0.71223563534 rad
∠ C' = γ' = 76.1989603005° = 76°11'23″ = 1.81218332254 rad

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How did we calculate this triangle?

a = 155 ; ; b = 175 ; ; c = 260 ; ;

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

p = a+b+c = 155+175+260 = 590 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 590 }{ 2 } = 295 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 295 * (295-155)(295-175)(295-260) } ; ; T = sqrt{ 173460000 } = 13170.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13170.42 }{ 155 } = 169.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13170.42 }{ 175 } = 150.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13170.42 }{ 260 } = 101.31 ; ;

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{ 155**2-175**2-260**2 }{ 2 * 175 * 260 } ) = 35° 22'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 175**2-155**2-260**2 }{ 2 * 155 * 260 } ) = 40° 48'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 260**2-155**2-175**2 }{ 2 * 175 * 155 } ) = 103° 48'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13170.42 }{ 295 } = 44.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 155 }{ 2 * sin 35° 22'29" } = 133.87 ; ;




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