16 23 27 triangle

Acute scalene triangle.

Sides: a = 16   b = 23   c = 27

Area: T = 183.4676618217
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 36.21991096219° = 36°13'9″ = 0.6322142715 rad
Angle ∠ B = β = 58.1454569176° = 58°8'40″ = 1.01548141743 rad
Angle ∠ C = γ = 85.63663212021° = 85°38'11″ = 1.49546357643 rad

Height: ha = 22.93333272771
Height: hb = 15.95436189754
Height: hc = 13.59901198679

Median: ma = 23.7769728648
Median: mb = 18.98802528961
Median: mc = 14.5

Inradius: r = 5.56595944914
Circumradius: R = 13.53992477615

Vertex coordinates: A[27; 0] B[0; 0] C[8.44444444444; 13.59901198679]
Centroid: CG[11.81548148148; 4.5330039956]
Coordinates of the circumscribed circle: U[13.5; 1.03301601558]
Coordinates of the inscribed circle: I[10; 5.56595944914]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.7810890378° = 143°46'51″ = 0.6322142715 rad
∠ B' = β' = 121.8555430824° = 121°51'20″ = 1.01548141743 rad
∠ C' = γ' = 94.36436787979° = 94°21'49″ = 1.49546357643 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 = 23 ; ; c = 27 ; ;

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

p = a+b+c = 16+23+27 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-16)(33-23)(33-27) } ; ; T = sqrt{ 33660 } = 183.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 183.47 }{ 16 } = 22.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 183.47 }{ 23 } = 15.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 183.47 }{ 27 } = 13.59 ; ;

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**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 36° 13'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 58° 8'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-16**2-23**2 }{ 2 * 23 * 16 } ) = 85° 38'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 183.47 }{ 33 } = 5.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 36° 13'9" } = 13.54 ; ;




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