6 15 17 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 15   c = 17

Area: T = 44.45222215418
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 20.40444519895° = 20°24'16″ = 0.35661248693 rad
Angle ∠ B = β = 60.64765299452° = 60°38'48″ = 1.05884816275 rad
Angle ∠ C = γ = 98.94990180653° = 98°56'56″ = 1.72769861569 rad

Height: ha = 14.81774071806
Height: hb = 5.92769628722
Height: hc = 5.23296731226

Median: ma = 15.7488015748
Median: mb = 10.3087764064
Median: mc = 7.63221687612

Inradius: r = 2.34395906075
Circumradius: R = 8.60547443015

Vertex coordinates: A[17; 0] B[0; 0] C[2.94111764706; 5.23296731226]
Centroid: CG[6.64770588235; 1.74332243742]
Coordinates of the circumscribed circle: U[8.5; -1.33985157802]
Coordinates of the inscribed circle: I[4; 2.34395906075]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.596554801° = 159°35'44″ = 0.35661248693 rad
∠ B' = β' = 119.3533470055° = 119°21'12″ = 1.05884816275 rad
∠ C' = γ' = 81.05109819347° = 81°3'4″ = 1.72769861569 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 = 6 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 6+15+17 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-6)(19-15)(19-17) } ; ; T = sqrt{ 1976 } = 44.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.45 }{ 6 } = 14.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.45 }{ 15 } = 5.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.45 }{ 17 } = 5.23 ; ;

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{ 15**2+17**2-6**2 }{ 2 * 15 * 17 } ) = 20° 24'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+17**2-15**2 }{ 2 * 6 * 17 } ) = 60° 38'48" ; ; gamma = 180° - alpha - beta = 180° - 20° 24'16" - 60° 38'48" = 98° 56'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.45 }{ 19 } = 2.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 20° 24'16" } = 8.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 17**2 - 6**2 } }{ 2 } = 15.748 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17**2+2 * 6**2 - 15**2 } }{ 2 } = 10.308 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15**2+2 * 6**2 - 17**2 } }{ 2 } = 7.632 ; ;
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