170 366 427 triangle

Obtuse scalene triangle.

Sides: a = 170   b = 366   c = 427

Area: T = 30726.73549703
Perimeter: p = 963
Semiperimeter: s = 481.5

Angle ∠ A = α = 23.15551106019° = 23°9'18″ = 0.40441329187 rad
Angle ∠ B = β = 57.84219547775° = 57°50'31″ = 1.01095325567 rad
Angle ∠ C = γ = 99.00329346206° = 99°11″ = 1.72879271783 rad

Height: ha = 361.4910999651
Height: hb = 167.9065655576
Height: hc = 143.9199133351

Median: ma = 388.4811016267
Median: mb = 268.5621910926
Median: mc = 189.3329738816

Inradius: r = 63.81546105303
Circumradius: R = 216.163305821

Vertex coordinates: A[427; 0] B[0; 0] C[90.48436065574; 143.9199133351]
Centroid: CG[172.4954535519; 47.97330444502]
Coordinates of the circumscribed circle: U[213.5; -33.82662876288]
Coordinates of the inscribed circle: I[115.5; 63.81546105303]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.8454889398° = 156°50'42″ = 0.40441329187 rad
∠ B' = β' = 122.1588045222° = 122°9'29″ = 1.01095325567 rad
∠ C' = γ' = 80.99770653794° = 80°59'49″ = 1.72879271783 rad

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How did we calculate this triangle?

a = 170 ; ; b = 366 ; ; c = 427 ; ;

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

p = a+b+c = 170+366+427 = 963 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 963 }{ 2 } = 481.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 481.5 * (481.5-170)(481.5-366)(481.5-427) } ; ; T = sqrt{ 944132241.94 } = 30726.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30726.73 }{ 170 } = 361.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30726.73 }{ 366 } = 167.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30726.73 }{ 427 } = 143.92 ; ;

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{ 366**2+427**2-170**2 }{ 2 * 366 * 427 } ) = 23° 9'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 170**2+427**2-366**2 }{ 2 * 170 * 427 } ) = 57° 50'31" ; ; gamma = 180° - alpha - beta = 180° - 23° 9'18" - 57° 50'31" = 99° 11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30726.73 }{ 481.5 } = 63.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 170 }{ 2 * sin 23° 9'18" } = 216.16 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 366**2+2 * 427**2 - 170**2 } }{ 2 } = 388.481 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 427**2+2 * 170**2 - 366**2 } }{ 2 } = 268.562 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 366**2+2 * 170**2 - 427**2 } }{ 2 } = 189.33 ; ;
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