22 29 29 triangle

Acute isosceles triangle.

Sides: a = 22   b = 29   c = 29

Area: T = 295.161097303
Perimeter: p = 80
Semiperimeter: s = 40

Angle ∠ A = α = 44.58219407495° = 44°34'55″ = 0.7788101653 rad
Angle ∠ B = β = 67.70990296252° = 67°42'33″ = 1.18217455003 rad
Angle ∠ C = γ = 67.70990296252° = 67°42'33″ = 1.18217455003 rad

Height: ha = 26.833281573
Height: hb = 20.35659291745
Height: hc = 20.35659291745

Median: ma = 26.833281573
Median: mb = 21.26661703181
Median: mc = 21.26661703181

Inradius: r = 7.37990243257
Circumradius: R = 15.67111097423

Vertex coordinates: A[29; 0] B[0; 0] C[8.34548275862; 20.35659291745]
Centroid: CG[12.44882758621; 6.78553097248]
Coordinates of the circumscribed circle: U[14.5; 5.94442140402]
Coordinates of the inscribed circle: I[11; 7.37990243257]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.418805925° = 135°25'5″ = 0.7788101653 rad
∠ B' = β' = 112.2910970375° = 112°17'27″ = 1.18217455003 rad
∠ C' = γ' = 112.2910970375° = 112°17'27″ = 1.18217455003 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 = 22 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 22+29+29 = 80 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 80 }{ 2 } = 40 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40 * (40-22)(40-29)(40-29) } ; ; T = sqrt{ 87120 } = 295.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 295.16 }{ 22 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 295.16 }{ 29 } = 20.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 295.16 }{ 29 } = 20.36 ; ;

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{ 22**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 44° 34'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 67° 42'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-29**2 }{ 2 * 29 * 22 } ) = 67° 42'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 295.16 }{ 40 } = 7.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 44° 34'55" } = 15.67 ; ;




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