16 29 29 triangle

Acute isosceles triangle.

Sides: a = 16   b = 29   c = 29

Area: T = 222.9987757836
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 32.02767888479° = 32°1'36″ = 0.55989729142 rad
Angle ∠ B = β = 73.98766055761° = 73°59'12″ = 1.29113098697 rad
Angle ∠ C = γ = 73.98766055761° = 73°59'12″ = 1.29113098697 rad

Height: ha = 27.87547197295
Height: hb = 15.37991557128
Height: hc = 15.37991557128

Median: ma = 27.87547197295
Median: mb = 18.39215741577
Median: mc = 18.39215741577

Inradius: r = 6.0276966428
Circumradius: R = 15.08553534701

Vertex coordinates: A[29; 0] B[0; 0] C[4.41437931034; 15.37991557128]
Centroid: CG[11.13879310345; 5.12663852376]
Coordinates of the circumscribed circle: U[14.5; 4.16114768193]
Coordinates of the inscribed circle: I[8; 6.0276966428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.9733211152° = 147°58'24″ = 0.55989729142 rad
∠ B' = β' = 106.0133394424° = 106°48″ = 1.29113098697 rad
∠ C' = γ' = 106.0133394424° = 106°48″ = 1.29113098697 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 = 16 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 16+29+29 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-16)(37-29)(37-29) } ; ; T = sqrt{ 49728 } = 223 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 223 }{ 16 } = 27.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 223 }{ 29 } = 15.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 223 }{ 29 } = 15.38 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 29**2+29**2-16**2 }{ 2 * 29 * 29 } ) = 32° 1'36" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+29**2-29**2 }{ 2 * 16 * 29 } ) = 73° 59'12" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 16**2+29**2-29**2 }{ 2 * 16 * 29 } ) = 73° 59'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 223 }{ 37 } = 6.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 32° 1'36" } = 15.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 29**2 - 16**2 } }{ 2 } = 27.875 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 16**2 - 29**2 } }{ 2 } = 18.392 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 16**2 - 29**2 } }{ 2 } = 18.392 ; ;
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