7 23 27 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 23   c = 27

Area: T = 71.1099841772
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 13.23773216903° = 13°14'14″ = 0.23110348476 rad
Angle ∠ B = β = 48.79769007607° = 48°47'49″ = 0.8521666583 rad
Angle ∠ C = γ = 117.9665777549° = 117°57'57″ = 2.05988912229 rad

Height: ha = 20.31442405063
Height: hb = 6.18325949367
Height: hc = 5.26766549461

Median: ma = 24.83444518764
Median: mb = 16.0233420359
Median: mc = 10.33219891599

Inradius: r = 2.49547312902
Circumradius: R = 15.28548441419

Vertex coordinates: A[27; 0] B[0; 0] C[4.61111111111; 5.26766549461]
Centroid: CG[10.5377037037; 1.75655516487]
Coordinates of the circumscribed circle: U[13.5; -7.16877374703]
Coordinates of the inscribed circle: I[5.5; 2.49547312902]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.763267831° = 166°45'46″ = 0.23110348476 rad
∠ B' = β' = 131.2033099239° = 131°12'11″ = 0.8521666583 rad
∠ C' = γ' = 62.03442224509° = 62°2'3″ = 2.05988912229 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 = 7 ; ; b = 23 ; ; c = 27 ; ;

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

p = a+b+c = 7+23+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 * (28.5-7)(28.5-23)(28.5-27) } ; ; T = sqrt{ 5055.19 } = 71.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 71.1 }{ 7 } = 20.31 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 71.1 }{ 23 } = 6.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 71.1 }{ 27 } = 5.27 ; ;

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{ 7**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 13° 14'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-7**2-27**2 }{ 2 * 7 * 27 } ) = 48° 47'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-7**2-23**2 }{ 2 * 23 * 7 } ) = 117° 57'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 71.1 }{ 28.5 } = 2.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 14'14" } = 15.28 ; ;




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