15 28 29 triangle

Acute scalene triangle.

Sides: a = 15   b = 28   c = 29

Area: T = 205.7577138394
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 30.45503140214° = 30°27'1″ = 0.53114582379 rad
Angle ∠ B = β = 71.08766450115° = 71°5'12″ = 1.24106960096 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 27.43442851192
Height: hb = 14.69769384567
Height: hc = 14.19901474754

Median: ma = 27.5
Median: mb = 18.35875597507
Median: mc = 17.15437167984

Inradius: r = 5.71554760665
Circumradius: R = 14.79990005293

Vertex coordinates: A[29; 0] B[0; 0] C[4.86220689655; 14.19901474754]
Centroid: CG[11.28773563218; 4.73300491585]
Coordinates of the circumscribed circle: U[14.5; 2.96598001059]
Coordinates of the inscribed circle: I[8; 5.71554760665]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.5549685979° = 149°32'59″ = 0.53114582379 rad
∠ B' = β' = 108.9133354989° = 108°54'48″ = 1.24106960096 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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 = 15 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 15+28+29 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-15)(36-28)(36-29) } ; ; T = sqrt{ 42336 } = 205.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 205.76 }{ 15 } = 27.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 205.76 }{ 28 } = 14.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 205.76 }{ 29 } = 14.19 ; ;

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{ 15**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 30° 27'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 71° 5'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-28**2 }{ 2 * 28 * 15 } ) = 78° 27'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 205.76 }{ 36 } = 5.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 30° 27'1" } = 14.8 ; ;




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