13 29 29 triangle

Acute isosceles triangle.

Sides: a = 13   b = 29   c = 29

Area: T = 183.7044075894
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 25.90443811917° = 25°54'16″ = 0.45221167425 rad
Angle ∠ B = β = 77.04878094041° = 77°2'52″ = 1.34547379556 rad
Angle ∠ C = γ = 77.04878094041° = 77°2'52″ = 1.34547379556 rad

Height: ha = 28.26221655221
Height: hb = 12.66992466134
Height: hc = 12.66992466134

Median: ma = 28.26221655221
Median: mb = 17.16882847134
Median: mc = 17.16882847134

Inradius: r = 5.17547627012
Circumradius: R = 14.87985484846

Vertex coordinates: A[29; 0] B[0; 0] C[2.91437931034; 12.66992466134]
Centroid: CG[10.63879310345; 4.22330822045]
Coordinates of the circumscribed circle: U[14.5; 3.33548470741]
Coordinates of the inscribed circle: I[6.5; 5.17547627012]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.0965618808° = 154°5'44″ = 0.45221167425 rad
∠ B' = β' = 102.9522190596° = 102°57'8″ = 1.34547379556 rad
∠ C' = γ' = 102.9522190596° = 102°57'8″ = 1.34547379556 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 = 13 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 13+29+29 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-13)(35.5-29)(35.5-29) } ; ; T = sqrt{ 33747.19 } = 183.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 183.7 }{ 13 } = 28.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 183.7 }{ 29 } = 12.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 183.7 }{ 29 } = 12.67 ; ;

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{ 13**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 25° 54'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-13**2-29**2 }{ 2 * 13 * 29 } ) = 77° 2'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-13**2-29**2 }{ 2 * 29 * 13 } ) = 77° 2'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 183.7 }{ 35.5 } = 5.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 25° 54'16" } = 14.88 ; ;




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