12 29 29 triangle

Acute isosceles triangle.

Sides: a = 12   b = 29   c = 29

Area: T = 170.2355131509
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 23.88110879212° = 23°52'52″ = 0.41768036132 rad
Angle ∠ B = β = 78.05994560394° = 78°3'34″ = 1.36223945202 rad
Angle ∠ C = γ = 78.05994560394° = 78°3'34″ = 1.36223945202 rad

Height: ha = 28.37325219182
Height: hb = 11.74403538972
Height: hc = 11.74403538972

Median: ma = 28.37325219182
Median: mb = 16.88002976164
Median: mc = 16.88002976164

Inradius: r = 4.86438609003
Circumradius: R = 14.82106775983

Vertex coordinates: A[29; 0] B[0; 0] C[2.48327586207; 11.74403538972]
Centroid: CG[10.49442528736; 3.91334512991]
Coordinates of the circumscribed circle: U[14.5; 3.06663470893]
Coordinates of the inscribed circle: I[6; 4.86438609003]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.1198912079° = 156°7'8″ = 0.41768036132 rad
∠ B' = β' = 101.9410543961° = 101°56'26″ = 1.36223945202 rad
∠ C' = γ' = 101.9410543961° = 101°56'26″ = 1.36223945202 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 = 12 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 12+29+29 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-12)(35-29)(35-29) } ; ; T = sqrt{ 28980 } = 170.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 170.24 }{ 12 } = 28.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 170.24 }{ 29 } = 11.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 170.24 }{ 29 } = 11.74 ; ;

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{ 12**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 23° 52'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-12**2-29**2 }{ 2 * 12 * 29 } ) = 78° 3'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-12**2-29**2 }{ 2 * 29 * 12 } ) = 78° 3'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 170.24 }{ 35 } = 4.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 23° 52'52" } = 14.82 ; ;




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