6 25 27 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 25   c = 27

Area: T = 73.0487929471
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 12.54999234492° = 12°30' = 0.21881648204 rad
Angle ∠ B = β = 64.39991730166° = 64°23'57″ = 1.12439776047 rad
Angle ∠ C = γ = 103.1010903534° = 103°6'3″ = 1.79994502285 rad

Height: ha = 24.34993098237
Height: hb = 5.84438343577
Height: hc = 5.41109577386

Median: ma = 25.84656959666
Median: mb = 15.04216089565
Median: mc = 12.17657956619

Inradius: r = 2.51988941197
Circumradius: R = 13.86107624793

Vertex coordinates: A[27; 0] B[0; 0] C[2.59325925926; 5.41109577386]
Centroid: CG[9.86441975309; 1.80436525795]
Coordinates of the circumscribed circle: U[13.5; -3.14217728286]
Coordinates of the inscribed circle: I[4; 2.51988941197]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.5500076551° = 167°30' = 0.21881648204 rad
∠ B' = β' = 115.6010826983° = 115°36'3″ = 1.12439776047 rad
∠ C' = γ' = 76.89990964657° = 76°53'57″ = 1.79994502285 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 = 6 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 6+25+27 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-6)(29-25)(29-27) } ; ; T = sqrt{ 5336 } = 73.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73.05 }{ 6 } = 24.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73.05 }{ 25 } = 5.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73.05 }{ 27 } = 5.41 ; ;

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{ 6**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 12° 30' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-6**2-27**2 }{ 2 * 6 * 27 } ) = 64° 23'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-6**2-25**2 }{ 2 * 25 * 6 } ) = 103° 6'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73.05 }{ 29 } = 2.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 12° 30' } = 13.86 ; ;




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