14 16 22 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 16   c = 22

Area: T = 111.714392035
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 39.40105687537° = 39°24'2″ = 0.68876696519 rad
Angle ∠ B = β = 46.50333874881° = 46°30'12″ = 0.8121637225 rad
Angle ∠ C = γ = 94.09660437582° = 94°5'46″ = 1.64222857767 rad

Height: ha = 15.95991314786
Height: hb = 13.96442400438
Height: hc = 10.15658109409

Median: ma = 17.91664728672
Median: mb = 16.61332477258
Median: mc = 10.2476950766

Inradius: r = 4.29766892442
Circumradius: R = 11.02881690602

Vertex coordinates: A[22; 0] B[0; 0] C[9.63663636364; 10.15658109409]
Centroid: CG[10.54554545455; 3.38552703136]
Coordinates of the circumscribed circle: U[11; -0.78877263614]
Coordinates of the inscribed circle: I[10; 4.29766892442]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.5999431246° = 140°35'58″ = 0.68876696519 rad
∠ B' = β' = 133.4976612512° = 133°29'48″ = 0.8121637225 rad
∠ C' = γ' = 85.90439562418° = 85°54'14″ = 1.64222857767 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 = 16 ; ; c = 22 ; ;

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

p = a+b+c = 14+16+22 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-14)(26-16)(26-22) } ; ; T = sqrt{ 12480 } = 111.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 111.71 }{ 14 } = 15.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 111.71 }{ 16 } = 13.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 111.71 }{ 22 } = 10.16 ; ;

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**2-16**2-22**2 }{ 2 * 16 * 22 } ) = 39° 24'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 46° 30'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-16**2 }{ 2 * 16 * 14 } ) = 94° 5'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 111.71 }{ 26 } = 4.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 39° 24'2" } = 11.03 ; ;




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