16 28 28 triangle

Acute isosceles triangle.

Sides: a = 16   b = 28   c = 28

Area: T = 214.663252584
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 33.2033099198° = 33°12'11″ = 0.58795034029 rad
Angle ∠ B = β = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: ha = 26.833281573
Height: hb = 15.333303756
Height: hc = 15.333303756

Median: ma = 26.833281573
Median: mb = 18
Median: mc = 18

Inradius: r = 5.963284794
Circumradius: R = 14.6098977453

Vertex coordinates: A[28; 0] B[0; 0] C[4.57114285714; 15.333303756]
Centroid: CG[10.85771428571; 5.111101252]
Coordinates of the circumscribed circle: U[14; 4.1743993558]
Coordinates of the inscribed circle: I[8; 5.963284794]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7976900802° = 146°47'49″ = 0.58795034029 rad
∠ B' = β' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 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 = 16 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 16+28+28 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-16)(36-28)(36-28) } ; ; T = sqrt{ 46080 } = 214.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 214.66 }{ 16 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 214.66 }{ 28 } = 15.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 214.66 }{ 28 } = 15.33 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 28**2+28**2-16**2 }{ 2 * 28 * 28 } ) = 33° 12'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+28**2-28**2 }{ 2 * 16 * 28 } ) = 73° 23'54" ; ; gamma = 180° - alpha - beta = 180° - 33° 12'11" - 73° 23'54" = 73° 23'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 214.66 }{ 36 } = 5.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 33° 12'11" } = 14.61 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 28**2 - 16**2 } }{ 2 } = 26.833 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 16**2 - 28**2 } }{ 2 } = 18 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 16**2 - 28**2 } }{ 2 } = 18 ; ;
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