6 14 15 triangle

Acute scalene triangle.

Sides: a = 6   b = 14   c = 15

Area: T = 41.9643525829
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 23.55664643091° = 23°33'23″ = 0.41111378623 rad
Angle ∠ B = β = 68.83215511542° = 68°49'54″ = 1.20113371969 rad
Angle ∠ C = γ = 87.61219845367° = 87°36'43″ = 1.52991175944 rad

Height: ha = 13.9887841943
Height: hb = 5.99547894041
Height: hc = 5.59551367772

Median: ma = 14.19550695666
Median: mb = 9.02877350426
Median: mc = 7.73298124169

Inradius: r = 2.39879157617
Circumradius: R = 7.50765189061

Vertex coordinates: A[15; 0] B[0; 0] C[2.16766666667; 5.59551367772]
Centroid: CG[5.72222222222; 1.86550455924]
Coordinates of the circumscribed circle: U[7.5; 0.31327716211]
Coordinates of the inscribed circle: I[3.5; 2.39879157617]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.4443535691° = 156°26'37″ = 0.41111378623 rad
∠ B' = β' = 111.1688448846° = 111°10'6″ = 1.20113371969 rad
∠ C' = γ' = 92.38880154633° = 92°23'17″ = 1.52991175944 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 = 6 ; ; b = 14 ; ; c = 15 ; ;

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

p = a+b+c = 6+14+15 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-6)(17.5-14)(17.5-15) } ; ; T = sqrt{ 1760.94 } = 41.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 41.96 }{ 6 } = 13.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 41.96 }{ 14 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 41.96 }{ 15 } = 5.6 ; ;

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{ 6**2-14**2-15**2 }{ 2 * 14 * 15 } ) = 23° 33'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-6**2-15**2 }{ 2 * 6 * 15 } ) = 68° 49'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-6**2-14**2 }{ 2 * 14 * 6 } ) = 87° 36'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 41.96 }{ 17.5 } = 2.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 23° 33'23" } = 7.51 ; ;




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