5 28 28 triangle

Acute isosceles triangle.

Sides: a = 5   b = 28   c = 28

Area: T = 69.72204238369
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 10.24550321996° = 10°14'42″ = 0.17988095439 rad
Angle ∠ B = β = 84.87774839002° = 84°52'39″ = 1.48113915549 rad
Angle ∠ C = γ = 84.87774839002° = 84°52'39″ = 1.48113915549 rad

Height: ha = 27.88881695348
Height: hb = 4.98800302741
Height: hc = 4.98800302741

Median: ma = 27.88881695348
Median: mb = 14.44395290782
Median: mc = 14.44395290782

Inradius: r = 2.28659155356
Circumradius: R = 14.05661394505

Vertex coordinates: A[28; 0] B[0; 0] C[0.44664285714; 4.98800302741]
Centroid: CG[9.48221428571; 1.66600100914]
Coordinates of the circumscribed circle: U[14; 1.25550124509]
Coordinates of the inscribed circle: I[2.5; 2.28659155356]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.75549678° = 169°45'18″ = 0.17988095439 rad
∠ B' = β' = 95.12325160998° = 95°7'21″ = 1.48113915549 rad
∠ C' = γ' = 95.12325160998° = 95°7'21″ = 1.48113915549 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 = 5 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 5+28+28 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-5)(30.5-28)(30.5-28) } ; ; T = sqrt{ 4860.94 } = 69.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.72 }{ 5 } = 27.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.72 }{ 28 } = 4.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.72 }{ 28 } = 4.98 ; ;

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{ 5**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 10° 14'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-5**2-28**2 }{ 2 * 5 * 28 } ) = 84° 52'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-5**2-28**2 }{ 2 * 28 * 5 } ) = 84° 52'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.72 }{ 30.5 } = 2.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 14'42" } = 14.06 ; ;




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