16 17 26 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 17   c = 26

Area: T = 131.9987869301
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 36.67550126606° = 36°40'30″ = 0.64400997241 rad
Angle ∠ B = β = 39.39107046527° = 39°23'27″ = 0.68774974909 rad
Angle ∠ C = γ = 103.9344282687° = 103°56'3″ = 1.81439954386 rad

Height: ha = 16.54997336626
Height: hb = 15.52991610942
Height: hc = 10.15436822539

Median: ma = 20.45772725455
Median: mb = 19.8433134833
Median: mc = 10.17334949747

Inradius: r = 4.47545040441
Circumradius: R = 13.39441555978

Vertex coordinates: A[26; 0] B[0; 0] C[12.36553846154; 10.15436822539]
Centroid: CG[12.78884615385; 3.38545607513]
Coordinates of the circumscribed circle: U[13; -3.22554308517]
Coordinates of the inscribed circle: I[12.5; 4.47545040441]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.3254987339° = 143°19'30″ = 0.64400997241 rad
∠ B' = β' = 140.6099295347° = 140°36'33″ = 0.68774974909 rad
∠ C' = γ' = 76.06657173133° = 76°3'57″ = 1.81439954386 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 = 16 ; ; b = 17 ; ; c = 26 ; ;

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

p = a+b+c = 16+17+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-16)(29.5-17)(29.5-26) } ; ; T = sqrt{ 17423.44 } = 132 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 132 }{ 16 } = 16.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 132 }{ 17 } = 15.53 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 132 }{ 26 } = 10.15 ; ;

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{ 16**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 36° 40'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 39° 23'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 103° 56'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 132 }{ 29.5 } = 4.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 36° 40'30" } = 13.39 ; ;




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