7 22 27 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 22   c = 27

Area: T = 59.39769696197
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 11.53663623724° = 11°32'11″ = 0.20113475071 rad
Angle ∠ B = β = 38.9422441269° = 38°56'33″ = 0.68796738189 rad
Angle ∠ C = γ = 129.5211196359° = 129°31'16″ = 2.26105713276 rad

Height: ha = 16.97105627485
Height: hb = 5.43997245109
Height: hc = 4.43997755274

Median: ma = 24.37772434865
Median: mb = 16.37107055437
Median: mc = 9.17987798753

Inradius: r = 2.12113203436
Circumradius: R = 17.50108928344

Vertex coordinates: A[27; 0] B[0; 0] C[5.44444444444; 4.43997755274]
Centroid: CG[10.81548148148; 1.46765918425]
Coordinates of the circumscribed circle: U[13.5; -11.13769318037]
Coordinates of the inscribed circle: I[6; 2.12113203436]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.4643637628° = 168°27'49″ = 0.20113475071 rad
∠ B' = β' = 141.0587558731° = 141°3'27″ = 0.68796738189 rad
∠ C' = γ' = 50.47988036414° = 50°28'44″ = 2.26105713276 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 = 22 ; ; c = 27 ; ;

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

p = a+b+c = 7+22+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 * (28-7)(28-22)(28-27) } ; ; T = sqrt{ 3528 } = 59.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.4 }{ 7 } = 16.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.4 }{ 22 } = 5.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.4 }{ 27 } = 4.4 ; ;

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**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 11° 32'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-7**2-27**2 }{ 2 * 7 * 27 } ) = 38° 56'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-7**2-22**2 }{ 2 * 22 * 7 } ) = 129° 31'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.4 }{ 28 } = 2.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 11° 32'11" } = 17.5 ; ;




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