18 22 28 triangle

Acute scalene triangle.

Sides: a = 18   b = 22   c = 28

Area: T = 197.909907003
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 39.98331214543° = 39°58'59″ = 0.69878371146 rad
Angle ∠ B = β = 51.75333801217° = 51°45'12″ = 0.90332668822 rad
Angle ∠ C = γ = 88.26334984241° = 88°15'49″ = 1.54404886568 rad

Height: ha = 21.998989667
Height: hb = 17.99217336391
Height: hc = 14.1366362145

Median: ma = 23.51659520326
Median: mb = 20.80986520467
Median: mc = 14.42222051019

Inradius: r = 5.82108550009
Circumradius: R = 14.00664323458

Vertex coordinates: A[28; 0] B[0; 0] C[11.14328571429; 14.1366362145]
Centroid: CG[13.04876190476; 4.7122120715]
Coordinates of the circumscribed circle: U[14; 0.42444373438]
Coordinates of the inscribed circle: I[12; 5.82108550009]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.0176878546° = 140°1'1″ = 0.69878371146 rad
∠ B' = β' = 128.2476619878° = 128°14'48″ = 0.90332668822 rad
∠ C' = γ' = 91.73765015759° = 91°44'11″ = 1.54404886568 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 = 18 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 18+22+28 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-18)(34-22)(34-28) } ; ; T = sqrt{ 39168 } = 197.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 197.91 }{ 18 } = 21.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 197.91 }{ 22 } = 17.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 197.91 }{ 28 } = 14.14 ; ;

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{ 18**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 39° 58'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 51° 45'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-22**2 }{ 2 * 22 * 18 } ) = 88° 15'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 197.91 }{ 34 } = 5.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 39° 58'59" } = 14.01 ; ;




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