100 50 75 triangle

Obtuse scalene triangle.

Sides: a = 100   b = 50   c = 75

Area: T = 1815.461094353
Perimeter: p = 225
Semiperimeter: s = 112.5

Angle ∠ A = α = 104.4787512186° = 104°28'39″ = 1.82334765819 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 46.56774634422° = 46°34'3″ = 0.81327555614 rad

Height: ha = 36.30992188707
Height: hb = 72.61884377414
Height: hc = 48.41222918276

Median: ma = 39.52884707521
Median: mb = 84.77991247891
Median: mc = 69.59770545354

Inradius: r = 16.13774306092
Circumradius: R = 51.64397779494

Vertex coordinates: A[75; 0] B[0; 0] C[87.5; 48.41222918276]
Centroid: CG[54.16766666667; 16.13774306092]
Coordinates of the circumscribed circle: U[37.5; 35.50223473402]
Coordinates of the inscribed circle: I[62.5; 16.13774306092]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 75.52224878141° = 75°31'21″ = 1.82334765819 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 133.4332536558° = 133°25'57″ = 0.81327555614 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 = 100 ; ; b = 50 ; ; c = 75 ; ;

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

p = a+b+c = 100+50+75 = 225 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 225 }{ 2 } = 112.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 112.5 * (112.5-100)(112.5-50)(112.5-75) } ; ; T = sqrt{ 3295898.44 } = 1815.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1815.46 }{ 100 } = 36.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1815.46 }{ 50 } = 72.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1815.46 }{ 75 } = 48.41 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 50**2+75**2-100**2 }{ 2 * 50 * 75 } ) = 104° 28'39" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+75**2-50**2 }{ 2 * 100 * 75 } ) = 28° 57'18" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 100**2+50**2-75**2 }{ 2 * 100 * 50 } ) = 46° 34'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1815.46 }{ 112.5 } = 16.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 104° 28'39" } = 51.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 75**2 - 100**2 } }{ 2 } = 39.528 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 75**2+2 * 100**2 - 50**2 } }{ 2 } = 84.779 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 100**2 - 75**2 } }{ 2 } = 69.597 ; ;
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