197 208 299 triangle

Obtuse scalene triangle.

Sides: a = 197   b = 208   c = 299

Area: T = 20405.92985503
Perimeter: p = 704
Semiperimeter: s = 352

Angle ∠ A = α = 41.01224937709° = 41°45″ = 0.71658030508 rad
Angle ∠ B = β = 43.85773690016° = 43°51'27″ = 0.76554554903 rad
Angle ∠ C = γ = 95.13301372275° = 95°7'49″ = 1.66603341125 rad

Height: ha = 207.1676787313
Height: hb = 196.2110851445
Height: hc = 136.4954505353

Median: ma = 237.9711111692
Median: mb = 230.8444103238
Median: mc = 136.6987659087

Inradius: r = 57.9711387927
Circumradius: R = 150.1011280246

Vertex coordinates: A[299; 0] B[0; 0] C[142.0550167224; 136.4954505353]
Centroid: CG[147.0176722408; 45.49881684511]
Coordinates of the circumscribed circle: U[149.5; -13.42217856994]
Coordinates of the inscribed circle: I[144; 57.9711387927]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.9887506229° = 138°59'15″ = 0.71658030508 rad
∠ B' = β' = 136.1432630998° = 136°8'33″ = 0.76554554903 rad
∠ C' = γ' = 84.87698627725° = 84°52'11″ = 1.66603341125 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 = 197 ; ; b = 208 ; ; c = 299 ; ;

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

p = a+b+c = 197+208+299 = 704 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 704 }{ 2 } = 352 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 352 * (352-197)(352-208)(352-299) } ; ; T = sqrt{ 416401920 } = 20405.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20405.93 }{ 197 } = 207.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20405.93 }{ 208 } = 196.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20405.93 }{ 299 } = 136.49 ; ;

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{ 208**2+299**2-197**2 }{ 2 * 208 * 299 } ) = 41° 45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 197**2+299**2-208**2 }{ 2 * 197 * 299 } ) = 43° 51'27" ; ; gamma = 180° - alpha - beta = 180° - 41° 45" - 43° 51'27" = 95° 7'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20405.93 }{ 352 } = 57.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 197 }{ 2 * sin 41° 45" } = 150.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 208**2+2 * 299**2 - 197**2 } }{ 2 } = 237.971 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 299**2+2 * 197**2 - 208**2 } }{ 2 } = 230.844 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 208**2+2 * 197**2 - 299**2 } }{ 2 } = 136.698 ; ;
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