17 19 26 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 19   c = 26

Area: T = 161.3699142032
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 40.79221107438° = 40°47'32″ = 0.71219566413 rad
Angle ∠ B = β = 46.90112441381° = 46°54'4″ = 0.81985811335 rad
Angle ∠ C = γ = 92.30766451181° = 92°18'24″ = 1.61110548788 rad

Height: ha = 18.98546049449
Height: hb = 16.9866225477
Height: hc = 12.41330109255

Median: ma = 21.12546301743
Median: mb = 19.80553023203
Median: mc = 12.49899959968

Inradius: r = 5.20554561946
Circumradius: R = 13.01105420006

Vertex coordinates: A[26; 0] B[0; 0] C[11.61553846154; 12.41330109255]
Centroid: CG[12.53884615385; 4.13876703085]
Coordinates of the circumscribed circle: U[13; -0.52436441053]
Coordinates of the inscribed circle: I[12; 5.20554561946]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.2087889256° = 139°12'28″ = 0.71219566413 rad
∠ B' = β' = 133.0998755862° = 133°5'56″ = 0.81985811335 rad
∠ C' = γ' = 87.69333548819° = 87°41'36″ = 1.61110548788 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 = 19 ; ; c = 26 ; ;

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

p = a+b+c = 17+19+26 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-17)(31-19)(31-26) } ; ; T = sqrt{ 26040 } = 161.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161.37 }{ 17 } = 18.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161.37 }{ 19 } = 16.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161.37 }{ 26 } = 12.41 ; ;

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**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 40° 47'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 46° 54'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-19**2 }{ 2 * 19 * 17 } ) = 92° 18'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161.37 }{ 31 } = 5.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 40° 47'32" } = 13.01 ; ;




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