7 10 14 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 10   c = 14

Area: T = 32.96987351896
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 28.09880547134° = 28°5'53″ = 0.49904035682 rad
Angle ∠ B = β = 42.28659661512° = 42°17'9″ = 0.73880293367 rad
Angle ∠ C = γ = 109.6165979135° = 109°36'58″ = 1.91331597487 rad

Height: ha = 9.42196386256
Height: hb = 6.59437470379
Height: hc = 4.71098193128

Median: ma = 11.65111801977
Median: mb = 9.87442088291
Median: mc = 5.05497524692

Inradius: r = 2.12770151735
Circumradius: R = 7.43112829592

Vertex coordinates: A[14; 0] B[0; 0] C[5.17985714286; 4.71098193128]
Centroid: CG[6.39328571429; 1.57699397709]
Coordinates of the circumscribed circle: U[7; -2.49547878506]
Coordinates of the inscribed circle: I[5.5; 2.12770151735]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.9021945287° = 151°54'7″ = 0.49904035682 rad
∠ B' = β' = 137.7144033849° = 137°42'51″ = 0.73880293367 rad
∠ C' = γ' = 70.38440208646° = 70°23'2″ = 1.91331597487 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 = 7 ; ; b = 10 ; ; c = 14 ; ;

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

p = a+b+c = 7+10+14 = 31 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31 }{ 2 } = 15.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.5 * (15.5-7)(15.5-10)(15.5-14) } ; ; T = sqrt{ 1086.94 } = 32.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.97 }{ 7 } = 9.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.97 }{ 10 } = 6.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.97 }{ 14 } = 4.71 ; ;

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{ 7**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 28° 5'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-7**2-14**2 }{ 2 * 7 * 14 } ) = 42° 17'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-7**2-10**2 }{ 2 * 10 * 7 } ) = 109° 36'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.97 }{ 15.5 } = 2.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 28° 5'53" } = 7.43 ; ;




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