7 27 29 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 27   c = 29

Area: T = 93.17882565838
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 13.76987180931° = 13°46'7″ = 0.24403094645 rad
Angle ∠ B = β = 66.637721368° = 66°38'14″ = 1.16330387831 rad
Angle ∠ C = γ = 99.59440682269° = 99°35'39″ = 1.7388244406 rad

Height: ha = 26.62223590239
Height: hb = 6.90220930803
Height: hc = 6.4266086661

Median: ma = 27.79883812478
Median: mb = 16.21095650774
Median: mc = 13.37697419571

Inradius: r = 2.95880398915
Circumradius: R = 14.70656840323

Vertex coordinates: A[29; 0] B[0; 0] C[2.7765862069; 6.4266086661]
Centroid: CG[10.5921954023; 2.1422028887]
Coordinates of the circumscribed circle: U[14.5; -2.45109473387]
Coordinates of the inscribed circle: I[4.5; 2.95880398915]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.2311281907° = 166°13'53″ = 0.24403094645 rad
∠ B' = β' = 113.363278632° = 113°21'46″ = 1.16330387831 rad
∠ C' = γ' = 80.40659317731° = 80°24'21″ = 1.7388244406 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 = 27 ; ; c = 29 ; ;

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

p = a+b+c = 7+27+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-7)(31.5-27)(31.5-29) } ; ; T = sqrt{ 8682.19 } = 93.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 93.18 }{ 7 } = 26.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 93.18 }{ 27 } = 6.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 93.18 }{ 29 } = 6.43 ; ;

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**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 13° 46'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-7**2-29**2 }{ 2 * 7 * 29 } ) = 66° 38'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-7**2-27**2 }{ 2 * 27 * 7 } ) = 99° 35'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 93.18 }{ 31.5 } = 2.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 13° 46'7" } = 14.71 ; ;




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