16 16 28 triangle

Obtuse isosceles triangle.

Sides: a = 16   b = 16   c = 28

Area: T = 108.4443533694
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 122.0989951256° = 122°5'24″ = 2.1310871633 rad

Height: ha = 13.55554417117
Height: hb = 13.55554417117
Height: hc = 7.74659666924

Median: ma = 21.35441565041
Median: mb = 21.35441565041
Median: mc = 7.74659666924

Inradius: r = 3.61547844565
Circumradius: R = 16.52547289438

Vertex coordinates: A[28; 0] B[0; 0] C[14; 7.74659666924]
Centroid: CG[14; 2.58219888975]
Coordinates of the circumscribed circle: U[14; -8.77987622514]
Coordinates of the inscribed circle: I[14; 3.61547844565]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 57.91100487437° = 57°54'36″ = 2.1310871633 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 = 16 ; ; c = 28 ; ;

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

p = a+b+c = 16+16+28 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-16)(30-16)(30-28) } ; ; T = sqrt{ 11760 } = 108.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 108.44 }{ 16 } = 13.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 108.44 }{ 16 } = 13.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 108.44 }{ 28 } = 7.75 ; ;

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{ 16**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 28° 57'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 28° 57'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-16**2 }{ 2 * 16 * 16 } ) = 122° 5'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 108.44 }{ 30 } = 3.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 28° 57'18" } = 16.52 ; ;




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