17 22 28 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 22   c = 28

Area: T = 186.9879778318
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 37.37884643889° = 37°22'42″ = 0.65223772729 rad
Angle ∠ B = β = 51.77989202453° = 51°46'44″ = 0.90437126414 rad
Angle ∠ C = γ = 90.84326153658° = 90°50'33″ = 1.58655027393 rad

Height: ha = 21.99876209786
Height: hb = 16.99881616653
Height: hc = 13.35656984513

Median: ma = 23.7011265789
Median: mb = 20.38438171106
Median: mc = 13.80221737418

Inradius: r = 5.581148592
Circumradius: R = 14.00215140864

Vertex coordinates: A[28; 0] B[0; 0] C[10.51878571429; 13.35656984513]
Centroid: CG[12.83992857143; 4.45218994838]
Coordinates of the circumscribed circle: U[14; -0.20659046189]
Coordinates of the inscribed circle: I[11.5; 5.581148592]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6221535611° = 142°37'18″ = 0.65223772729 rad
∠ B' = β' = 128.2211079755° = 128°13'16″ = 0.90437126414 rad
∠ C' = γ' = 89.15773846342° = 89°9'27″ = 1.58655027393 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 = 17 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 17+22+28 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-17)(33.5-22)(33.5-28) } ; ; T = sqrt{ 34961.44 } = 186.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 186.98 }{ 17 } = 22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 186.98 }{ 22 } = 17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 186.98 }{ 28 } = 13.36 ; ;

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{ 17**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 37° 22'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 51° 46'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-22**2 }{ 2 * 22 * 17 } ) = 90° 50'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 186.98 }{ 33.5 } = 5.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 37° 22'42" } = 14 ; ;




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