14 14 22 triangle

Obtuse isosceles triangle.

Sides: a = 14   b = 14   c = 22

Area: T = 95.26327944163
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ B = β = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ C = γ = 103.5743578597° = 103°34'25″ = 1.80876999646 rad

Height: ha = 13.60989706309
Height: hb = 13.60989706309
Height: hc = 8.66602540378

Median: ma = 17.05987221092
Median: mb = 17.05987221092
Median: mc = 8.66602540378

Inradius: r = 3.81105117767
Circumradius: R = 11.31660652761

Vertex coordinates: A[22; 0] B[0; 0] C[11; 8.66602540378]
Centroid: CG[11; 2.88767513459]
Coordinates of the circumscribed circle: U[11; -2.65658112383]
Coordinates of the inscribed circle: I[11; 3.81105117767]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ B' = β' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ C' = γ' = 76.42664214035° = 76°25'35″ = 1.80876999646 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 = 14 ; ; c = 22 ; ;

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

p = a+b+c = 14+14+22 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-14)(25-14)(25-22) } ; ; T = sqrt{ 9075 } = 95.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.26 }{ 14 } = 13.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.26 }{ 14 } = 13.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.26 }{ 22 } = 8.66 ; ;

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**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 38° 12'48" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 38° 12'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 103° 34'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.26 }{ 25 } = 3.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 38° 12'48" } = 11.32 ; ;




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