2 16 17 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 16   c = 17

Area: T = 14.26331518256
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 6.02200291433° = 6°1'12″ = 0.10550693296 rad
Angle ∠ B = β = 57.03656126762° = 57°2'8″ = 0.99554592321 rad
Angle ∠ C = γ = 116.944435818° = 116°56'40″ = 2.04110640919 rad

Height: ha = 14.26331518256
Height: hb = 1.78328939782
Height: hc = 1.67880178618

Median: ma = 16.47772570533
Median: mb = 9.08329510623
Median: mc = 7.59993420768

Inradius: r = 0.81550372472
Circumradius: R = 9.53550594078

Vertex coordinates: A[17; 0] B[0; 0] C[1.08882352941; 1.67880178618]
Centroid: CG[6.02994117647; 0.55993392873]
Coordinates of the circumscribed circle: U[8.5; -4.32105737942]
Coordinates of the inscribed circle: I[1.5; 0.81550372472]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.9879970857° = 173°58'48″ = 0.10550693296 rad
∠ B' = β' = 122.9644387324° = 122°57'52″ = 0.99554592321 rad
∠ C' = γ' = 63.05656418195° = 63°3'20″ = 2.04110640919 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 = 2 ; ; b = 16 ; ; c = 17 ; ;

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

p = a+b+c = 2+16+17 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-2)(17.5-16)(17.5-17) } ; ; T = sqrt{ 203.44 } = 14.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.26 }{ 2 } = 14.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.26 }{ 16 } = 1.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.26 }{ 17 } = 1.68 ; ;

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{ 16**2+17**2-2**2 }{ 2 * 16 * 17 } ) = 6° 1'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2**2+17**2-16**2 }{ 2 * 2 * 17 } ) = 57° 2'8" ; ; gamma = 180° - alpha - beta = 180° - 6° 1'12" - 57° 2'8" = 116° 56'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.26 }{ 17.5 } = 0.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2 }{ 2 * sin 6° 1'12" } = 9.54 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 17**2 - 2**2 } }{ 2 } = 16.477 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 2**2 - 16**2 } }{ 2 } = 9.083 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 2**2 - 17**2 } }{ 2 } = 7.599 ; ;
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