16 17 28 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 17   c = 28

Area: T = 122.17217541
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 30.8865674594° = 30°53'8″ = 0.53990567134 rad
Angle ∠ B = β = 33.05326598356° = 33°3'10″ = 0.57768777407 rad
Angle ∠ C = γ = 116.062166557° = 116°3'42″ = 2.02656581996 rad

Height: ha = 15.27114692626
Height: hb = 14.37331475412
Height: hc = 8.72765538643

Median: ma = 21.73770651193
Median: mb = 21.16601039695
Median: mc = 8.74664278423

Inradius: r = 4.0065631282
Circumradius: R = 15.58546170338

Vertex coordinates: A[28; 0] B[0; 0] C[13.41107142857; 8.72765538643]
Centroid: CG[13.80435714286; 2.90988512881]
Coordinates of the circumscribed circle: U[14; -6.84769181453]
Coordinates of the inscribed circle: I[13.5; 4.0065631282]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.1144325406° = 149°6'52″ = 0.53990567134 rad
∠ B' = β' = 146.9477340164° = 146°56'50″ = 0.57768777407 rad
∠ C' = γ' = 63.93883344296° = 63°56'18″ = 2.02656581996 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 = 17 ; ; c = 28 ; ;

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

p = a+b+c = 16+17+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 * (30.5-16)(30.5-17)(30.5-28) } ; ; T = sqrt{ 14925.94 } = 122.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 122.17 }{ 16 } = 15.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 122.17 }{ 17 } = 14.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 122.17 }{ 28 } = 8.73 ; ;

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**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 30° 53'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 33° 3'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 116° 3'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 122.17 }{ 30.5 } = 4.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 30° 53'8" } = 15.58 ; ;




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