16 26 28 triangle

Acute scalene triangle.

Sides: a = 16   b = 26   c = 28

Area: T = 204.6832681241
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 34.21660511313° = 34°12'58″ = 0.59771827493 rad
Angle ∠ B = β = 66.03105176822° = 66°1'50″ = 1.15224499404 rad
Angle ∠ C = γ = 79.75334311865° = 79°45'12″ = 1.3921959964 rad

Height: ha = 25.58553351551
Height: hb = 15.74548216339
Height: hc = 14.62201915172

Median: ma = 25.80769758011
Median: mb = 18.73549939952
Median: mc = 16.43216767252

Inradius: r = 5.84880766069
Circumradius: R = 14.22768998156

Vertex coordinates: A[28; 0] B[0; 0] C[6.5; 14.62201915172]
Centroid: CG[11.5; 4.87333971724]
Coordinates of the circumscribed circle: U[14; 2.53107466018]
Coordinates of the inscribed circle: I[9; 5.84880766069]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.7843948869° = 145°47'2″ = 0.59771827493 rad
∠ B' = β' = 113.9699482318° = 113°58'10″ = 1.15224499404 rad
∠ C' = γ' = 100.2476568814° = 100°14'48″ = 1.3921959964 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 = 26 ; ; c = 28 ; ;

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

p = a+b+c = 16+26+28 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-16)(35-26)(35-28) } ; ; T = sqrt{ 41895 } = 204.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 204.68 }{ 16 } = 25.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 204.68 }{ 26 } = 15.74 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 204.68 }{ 28 } = 14.62 ; ;

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**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 34° 12'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 66° 1'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-26**2 }{ 2 * 26 * 16 } ) = 79° 45'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 204.68 }{ 35 } = 5.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 34° 12'58" } = 14.23 ; ;




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