4 27 29 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 27   c = 29

Area: T = 48.37435464898
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 7.09875766618° = 7°5'51″ = 0.12438760817 rad
Angle ∠ B = β = 56.5154623377° = 56°30'53″ = 0.98663662535 rad
Angle ∠ C = γ = 116.3887799961° = 116°23'16″ = 2.03113503185 rad

Height: ha = 24.18767732449
Height: hb = 3.58332256659
Height: hc = 3.33661066545

Median: ma = 27.9466377225
Median: mb = 15.69223548265
Median: mc = 12.73877392029

Inradius: r = 1.61224515497
Circumradius: R = 16.18765328639

Vertex coordinates: A[29; 0] B[0; 0] C[2.20768965517; 3.33661066545]
Centroid: CG[10.40222988506; 1.11220355515]
Coordinates of the circumscribed circle: U[14.5; -7.19440146062]
Coordinates of the inscribed circle: I[3; 1.61224515497]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.9022423338° = 172°54'9″ = 0.12438760817 rad
∠ B' = β' = 123.4855376623° = 123°29'7″ = 0.98663662535 rad
∠ C' = γ' = 63.61222000388° = 63°36'44″ = 2.03113503185 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 = 4 ; ; b = 27 ; ; c = 29 ; ;

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

p = a+b+c = 4+27+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-4)(30-27)(30-29) } ; ; T = sqrt{ 2340 } = 48.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 48.37 }{ 4 } = 24.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 48.37 }{ 27 } = 3.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 48.37 }{ 29 } = 3.34 ; ;

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{ 4**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 7° 5'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-4**2-29**2 }{ 2 * 4 * 29 } ) = 56° 30'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-4**2-27**2 }{ 2 * 27 * 4 } ) = 116° 23'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 48.37 }{ 30 } = 1.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 7° 5'51" } = 16.19 ; ;




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