5 10 14 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 10   c = 14

Area: T = 17.60550418915
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 14.56663276483° = 14°33'59″ = 0.25442303774 rad
Angle ∠ B = β = 30.1998757023° = 30°11'56″ = 0.52770677401 rad
Angle ∠ C = γ = 135.2354915329° = 135°14'6″ = 2.36602945361 rad

Height: ha = 7.04220167566
Height: hb = 3.52110083783
Height: hc = 2.51550059845

Median: ma = 11.90658808998
Median: mb = 9.24766210045
Median: mc = 3.67442346142

Inradius: r = 1.21441408201
Circumradius: R = 9.94403341997

Vertex coordinates: A[14; 0] B[0; 0] C[4.32114285714; 2.51550059845]
Centroid: CG[6.10771428571; 0.83883353282]
Coordinates of the circumscribed circle: U[7; -7.05876372818]
Coordinates of the inscribed circle: I[4.5; 1.21441408201]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.4343672352° = 165°26'1″ = 0.25442303774 rad
∠ B' = β' = 149.8011242977° = 149°48'4″ = 0.52770677401 rad
∠ C' = γ' = 44.76550846713° = 44°45'54″ = 2.36602945361 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 = 5 ; ; b = 10 ; ; c = 14 ; ;

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

p = a+b+c = 5+10+14 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-5)(14.5-10)(14.5-14) } ; ; T = sqrt{ 309.94 } = 17.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.61 }{ 5 } = 7.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.61 }{ 10 } = 3.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.61 }{ 14 } = 2.52 ; ;

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{ 5**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 14° 33'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-5**2-14**2 }{ 2 * 5 * 14 } ) = 30° 11'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-5**2-10**2 }{ 2 * 10 * 5 } ) = 135° 14'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.61 }{ 14.5 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 14° 33'59" } = 9.94 ; ;




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