14 22 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 22   c = 28

Area: T = 151.7899327688
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 29.52662652473° = 29°31'35″ = 0.51553305444 rad
Angle ∠ B = β = 50.75438670503° = 50°45'14″ = 0.88658220881 rad
Angle ∠ C = γ = 99.72198677024° = 99°43'12″ = 1.74404400211 rad

Height: ha = 21.68441896697
Height: hb = 13.79990297898
Height: hc = 10.84220948349

Median: ma = 24.18767732449
Median: mb = 19.20993727123
Median: mc = 12

Inradius: r = 4.74334164903
Circumradius: R = 14.20438971569

Vertex coordinates: A[28; 0] B[0; 0] C[8.85771428571; 10.84220948349]
Centroid: CG[12.28657142857; 3.61440316116]
Coordinates of the circumscribed circle: U[14; -2.3988060559]
Coordinates of the inscribed circle: I[10; 4.74334164903]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4743734753° = 150°28'25″ = 0.51553305444 rad
∠ B' = β' = 129.246613295° = 129°14'46″ = 0.88658220881 rad
∠ C' = γ' = 80.28801322976° = 80°16'48″ = 1.74404400211 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 = 14 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 14+22+28 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-14)(32-22)(32-28) } ; ; T = sqrt{ 23040 } = 151.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.79 }{ 14 } = 21.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.79 }{ 22 } = 13.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.79 }{ 28 } = 10.84 ; ;

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{ 14**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 29° 31'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 50° 45'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-22**2 }{ 2 * 22 * 14 } ) = 99° 43'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.79 }{ 32 } = 4.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 29° 31'35" } = 14.2 ; ;




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