5 12 14 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 12   c = 14

Area: T = 29.23107629049
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 20.36441348063° = 20°21'51″ = 0.35554212017 rad
Angle ∠ B = β = 56.63329870308° = 56°37'59″ = 0.98884320889 rad
Angle ∠ C = γ = 103.0032878163° = 103°10″ = 1.7987739363 rad

Height: ha = 11.69223051619
Height: hb = 4.87217938175
Height: hc = 4.17658232721

Median: ma = 12.79664838921
Median: mb = 8.63113382508
Median: mc = 5.95881876439

Inradius: r = 1.88658556713
Circumradius: R = 7.18442120811

Vertex coordinates: A[14; 0] B[0; 0] C[2.75; 4.17658232721]
Centroid: CG[5.58333333333; 1.39219410907]
Coordinates of the circumscribed circle: U[7; -1.61664477182]
Coordinates of the inscribed circle: I[3.5; 1.88658556713]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.6365865194° = 159°38'9″ = 0.35554212017 rad
∠ B' = β' = 123.3677012969° = 123°22'1″ = 0.98884320889 rad
∠ C' = γ' = 76.99771218371° = 76°59'50″ = 1.7987739363 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 = 12 ; ; c = 14 ; ;

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

p = a+b+c = 5+12+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 * (15.5-5)(15.5-12)(15.5-14) } ; ; T = sqrt{ 854.44 } = 29.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.23 }{ 5 } = 11.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.23 }{ 12 } = 4.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.23 }{ 14 } = 4.18 ; ;

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**2-12**2-14**2 }{ 2 * 12 * 14 } ) = 20° 21'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12**2-5**2-14**2 }{ 2 * 5 * 14 } ) = 56° 37'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-5**2-12**2 }{ 2 * 12 * 5 } ) = 103° 10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.23 }{ 15.5 } = 1.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 20° 21'51" } = 7.18 ; ;




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