13 16 27 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 16   c = 27

Area: T = 70.99329573972
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 23.86109433465° = 23°51'39″ = 0.4166452024 rad
Angle ∠ C = γ = 136.95109202° = 136°57'3″ = 2.39902444711 rad

Height: ha = 10.92219934457
Height: hb = 8.87441196746
Height: hc = 5.2598737585

Median: ma = 21.21990951739
Median: mb = 19.62114168703
Median: mc = 5.5

Inradius: r = 2.53554627642
Circumradius: R = 19.77766095606

Vertex coordinates: A[27; 0] B[0; 0] C[11.88988888889; 5.2598737585]
Centroid: CG[12.9632962963; 1.75329125283]
Coordinates of the circumscribed circle: U[13.5; -14.45221377559]
Coordinates of the inscribed circle: I[12; 2.53554627642]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 156.1399056653° = 156°8'21″ = 0.4166452024 rad
∠ C' = γ' = 43.04990798002° = 43°2'57″ = 2.39902444711 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 = 16 ; ; c = 27 ; ;

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

p = a+b+c = 13+16+27 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-13)(28-16)(28-27) } ; ; T = sqrt{ 5040 } = 70.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.99 }{ 13 } = 10.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.99 }{ 16 } = 8.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.99 }{ 27 } = 5.26 ; ;

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**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 19° 11'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-13**2-27**2 }{ 2 * 13 * 27 } ) = 23° 51'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-13**2-16**2 }{ 2 * 16 * 13 } ) = 136° 57'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.99 }{ 28 } = 2.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 19° 11'17" } = 19.78 ; ;




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