13 17 27 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 17   c = 27

Area: T = 87.29436853386
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 22.35662712474° = 22°21'23″ = 0.39901905417 rad
Angle ∠ B = β = 29.82881284312° = 29°49'41″ = 0.52105990508 rad
Angle ∠ C = γ = 127.8165600321° = 127°48'56″ = 2.2310803061 rad

Height: ha = 13.43297977444
Height: hb = 10.2769845334
Height: hc = 6.4666198914

Median: ma = 21.60443977005
Median: mb = 19.41100489438
Median: mc = 6.83773971656

Inradius: r = 3.06329363277
Circumradius: R = 17.0898864953

Vertex coordinates: A[27; 0] B[0; 0] C[11.27877777778; 6.4666198914]
Centroid: CG[12.75992592593; 2.1555399638]
Coordinates of the circumscribed circle: U[13.5; -10.47875619961]
Coordinates of the inscribed circle: I[11.5; 3.06329363277]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6443728753° = 157°38'37″ = 0.39901905417 rad
∠ B' = β' = 150.1721871569° = 150°10'19″ = 0.52105990508 rad
∠ C' = γ' = 52.18443996786° = 52°11'4″ = 2.2310803061 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 = 13 ; ; b = 17 ; ; c = 27 ; ;

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

p = a+b+c = 13+17+27 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-13)(28.5-17)(28.5-27) } ; ; T = sqrt{ 7620.19 } = 87.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 87.29 }{ 13 } = 13.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 87.29 }{ 17 } = 10.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 87.29 }{ 27 } = 6.47 ; ;

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{ 13**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 22° 21'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-13**2-27**2 }{ 2 * 13 * 27 } ) = 29° 49'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-13**2-17**2 }{ 2 * 17 * 13 } ) = 127° 48'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 87.29 }{ 28.5 } = 3.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 22° 21'23" } = 17.09 ; ;




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