200 180 25.12 triangle

Obtuse scalene triangle.

Sides: a = 200   b = 180   c = 25.12

Area: T = 1440.762164638
Perimeter: p = 405.12
Semiperimeter: s = 202.56

Angle ∠ A = α = 140.4110738478° = 140°24'39″ = 2.45106296916 rad
Angle ∠ B = β = 34.9988263591° = 34°59'54″ = 0.61108349321 rad
Angle ∠ C = γ = 4.59109979312° = 4°35'28″ = 0.08801280299 rad

Height: ha = 14.40876164638
Height: hb = 16.00884627376
Height: hc = 114.7110322164

Median: ma = 80.71986917634
Median: mb = 110.5243785675
Median: mc = 189.8487956007

Inradius: r = 7.11327648419
Circumradius: R = 156.9177003286

Vertex coordinates: A[25.12; 0] B[0; 0] C[163.834388535; 114.7110322164]
Centroid: CG[62.98546284501; 38.23767740547]
Coordinates of the circumscribed circle: U[12.56; 156.4143529851]
Coordinates of the inscribed circle: I[22.56; 7.11327648419]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 39.58992615221° = 39°35'21″ = 2.45106296916 rad
∠ B' = β' = 145.0021736409° = 145°6″ = 0.61108349321 rad
∠ C' = γ' = 175.4099002069° = 175°24'32″ = 0.08801280299 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 = 200 ; ; b = 180 ; ; c = 25.12 ; ;

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

p = a+b+c = 200+180+25.12 = 405.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 405.12 }{ 2 } = 202.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 202.56 * (202.56-200)(202.56-180)(202.56-25.12) } ; ; T = sqrt{ 2075794.12 } = 1440.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1440.76 }{ 200 } = 14.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1440.76 }{ 180 } = 16.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1440.76 }{ 25.12 } = 114.71 ; ;

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{ 180**2+25.12**2-200**2 }{ 2 * 180 * 25.12 } ) = 140° 24'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+25.12**2-180**2 }{ 2 * 200 * 25.12 } ) = 34° 59'54" ; ;
 gamma = 180° - alpha - beta = 180° - 140° 24'39" - 34° 59'54" = 4° 35'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1440.76 }{ 202.56 } = 7.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 140° 24'39" } = 156.92 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 25.12**2 - 200**2 } }{ 2 } = 80.719 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.12**2+2 * 200**2 - 180**2 } }{ 2 } = 110.524 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 180**2+2 * 200**2 - 25.12**2 } }{ 2 } = 189.848 ; ;
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