9 28 28 triangle

Acute isosceles triangle.

Sides: a = 9   b = 28   c = 28

Area: T = 124.3622122449
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 18.49767166758° = 18°29'48″ = 0.32328286068 rad
Angle ∠ B = β = 80.75216416621° = 80°45'6″ = 1.40993820234 rad
Angle ∠ C = γ = 80.75216416621° = 80°45'6″ = 1.40993820234 rad

Height: ha = 27.63660272109
Height: hb = 8.88330087464
Height: hc = 8.88330087464

Median: ma = 27.63660272109
Median: mb = 15.37985564992
Median: mc = 15.37985564992

Inradius: r = 3.82765268446
Circumradius: R = 14.18443831969

Vertex coordinates: A[28; 0] B[0; 0] C[1.44664285714; 8.88330087464]
Centroid: CG[9.81554761905; 2.96110029155]
Coordinates of the circumscribed circle: U[14; 2.28796330138]
Coordinates of the inscribed circle: I[4.5; 3.82765268446]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5033283324° = 161°30'12″ = 0.32328286068 rad
∠ B' = β' = 99.24883583379° = 99°14'54″ = 1.40993820234 rad
∠ C' = γ' = 99.24883583379° = 99°14'54″ = 1.40993820234 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 = 9 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 9+28+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-9)(32.5-28)(32.5-28) } ; ; T = sqrt{ 15465.94 } = 124.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.36 }{ 9 } = 27.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.36 }{ 28 } = 8.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.36 }{ 28 } = 8.88 ; ;

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{ 9**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 18° 29'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-9**2-28**2 }{ 2 * 9 * 28 } ) = 80° 45'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-9**2-28**2 }{ 2 * 28 * 9 } ) = 80° 45'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.36 }{ 32.5 } = 3.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 18° 29'48" } = 14.18 ; ;




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