17 20 27 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 20   c = 27

Area: T = 169.7065627485
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ B = β = 47.68552720476° = 47°41'7″ = 0.83222650019 rad
Angle ∠ C = γ = 93.37222866834° = 93°22'20″ = 1.63296538327 rad

Height: ha = 19.96553679394
Height: hb = 16.97105627485
Height: hc = 12.57107872211

Median: ma = 22.18767077323
Median: mb = 20.22437484162
Median: mc = 12.73877392029

Inradius: r = 5.30333008589
Circumradius: R = 13.52334171902

Vertex coordinates: A[27; 0] B[0; 0] C[11.44444444444; 12.57107872211]
Centroid: CG[12.81548148148; 4.1990262407]
Coordinates of the circumscribed circle: U[13.5; -0.79554951288]
Coordinates of the inscribed circle: I[12; 5.30333008589]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ B' = β' = 132.3154727952° = 132°18'53″ = 0.83222650019 rad
∠ C' = γ' = 86.62877133166° = 86°37'40″ = 1.63296538327 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 = 17 ; ; b = 20 ; ; c = 27 ; ;

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

p = a+b+c = 17+20+27 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-17)(32-20)(32-27) } ; ; T = sqrt{ 28800 } = 169.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 169.71 }{ 17 } = 19.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 169.71 }{ 20 } = 16.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 169.71 }{ 27 } = 12.57 ; ;

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{ 17**2-20**2-27**2 }{ 2 * 20 * 27 } ) = 38° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 47° 41'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-17**2-20**2 }{ 2 * 20 * 17 } ) = 93° 22'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 169.71 }{ 32 } = 5.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 38° 56'33" } = 13.52 ; ;




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