16 22 28 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 22   c = 28

Area: T = 175.6565913649
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 34.77219440319° = 34°46'19″ = 0.60768849107 rad
Angle ∠ B = β = 51.64547342696° = 51°38'41″ = 0.90113706543 rad
Angle ∠ C = γ = 93.58333216985° = 93°35' = 1.63333370886 rad

Height: ha = 21.95769892062
Height: hb = 15.96987194227
Height: hc = 12.5476850975

Median: ma = 23.87546727726
Median: mb = 19.97549843554
Median: mc = 13.19109059583

Inradius: r = 5.32329064742
Circumradius: R = 14.02774241203

Vertex coordinates: A[28; 0] B[0; 0] C[9.92985714286; 12.5476850975]
Centroid: CG[12.64328571429; 4.18222836583]
Coordinates of the circumscribed circle: U[14; -0.87767140075]
Coordinates of the inscribed circle: I[11; 5.32329064742]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.2288055968° = 145°13'41″ = 0.60768849107 rad
∠ B' = β' = 128.355526573° = 128°21'19″ = 0.90113706543 rad
∠ C' = γ' = 86.41766783015° = 86°25' = 1.63333370886 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 = 22 ; ; c = 28 ; ;

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

p = a+b+c = 16+22+28 = 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)(33-22)(33-28) } ; ; T = sqrt{ 30855 } = 175.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 175.66 }{ 16 } = 21.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 175.66 }{ 22 } = 15.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 175.66 }{ 28 } = 12.55 ; ;

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**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 34° 46'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 51° 38'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-22**2 }{ 2 * 22 * 16 } ) = 93° 35' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 175.66 }{ 33 } = 5.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 34° 46'19" } = 14.03 ; ;




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