5 16 17 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 16   c = 17

Area: T = 39.95499687109
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 17.08325832434° = 17°4'57″ = 0.29881473223 rad
Angle ∠ B = β = 70.0511432774° = 70°3'5″ = 1.22326281476 rad
Angle ∠ C = γ = 92.86659839826° = 92°51'58″ = 1.62108171836 rad

Height: ha = 15.98799874844
Height: hb = 4.99437460889
Height: hc = 4.76999963189

Median: ma = 16.31771688721
Median: mb = 9.6443650761
Median: mc = 8.26113558209

Inradius: r = 2.10326299322
Circumradius: R = 8.51106449635

Vertex coordinates: A[17; 0] B[0; 0] C[1.70658823529; 4.76999963189]
Centroid: CG[6.23552941176; 1.56766654396]
Coordinates of the circumscribed circle: U[8.5; -0.42655322482]
Coordinates of the inscribed circle: I[3; 2.10326299322]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.9177416757° = 162°55'3″ = 0.29881473223 rad
∠ B' = β' = 109.9498567226° = 109°56'55″ = 1.22326281476 rad
∠ C' = γ' = 87.13440160174° = 87°8'2″ = 1.62108171836 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 = 5 ; ; b = 16 ; ; c = 17 ; ;

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

p = a+b+c = 5+16+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 * (19-5)(19-16)(19-17) } ; ; T = sqrt{ 1596 } = 39.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.95 }{ 5 } = 15.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.95 }{ 16 } = 4.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.95 }{ 17 } = 4.7 ; ;

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{ 5**2-16**2-17**2 }{ 2 * 16 * 17 } ) = 17° 4'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-5**2-17**2 }{ 2 * 5 * 17 } ) = 70° 3'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-5**2-16**2 }{ 2 * 16 * 5 } ) = 92° 51'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.95 }{ 19 } = 2.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 17° 4'57" } = 8.51 ; ;




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