2 14 15 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 14   c = 15

Area: T = 12.52774698164
Perimeter: p = 31
Semiperimeter: s = 15.5

Angle ∠ A = α = 6.8522238335° = 6°51'8″ = 0.12195941201 rad
Angle ∠ B = β = 56.63329870308° = 56°37'59″ = 0.98884320889 rad
Angle ∠ C = γ = 116.5154774634° = 116°30'53″ = 2.03435664446 rad

Height: ha = 12.52774698164
Height: hb = 1.79896385452
Height: hc = 1.67703293088

Median: ma = 14.47441148261
Median: mb = 8.09332070281
Median: mc = 6.61443782777

Inradius: r = 0.80882238591
Circumradius: R = 8.38215807612

Vertex coordinates: A[15; 0] B[0; 0] C[1.1; 1.67703293088]
Centroid: CG[5.36766666667; 0.55767764363]
Coordinates of the circumscribed circle: U[7.5; -3.74217771256]
Coordinates of the inscribed circle: I[1.5; 0.80882238591]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.1487761665° = 173°8'52″ = 0.12195941201 rad
∠ B' = β' = 123.3677012969° = 123°22'1″ = 0.98884320889 rad
∠ C' = γ' = 63.48552253657° = 63°29'7″ = 2.03435664446 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 = 2 ; ; b = 14 ; ; c = 15 ; ;

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

p = a+b+c = 2+14+15 = 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 * (15.5-2)(15.5-14)(15.5-15) } ; ; T = sqrt{ 156.94 } = 12.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.53 }{ 2 } = 12.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.53 }{ 14 } = 1.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.53 }{ 15 } = 1.67 ; ;

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{ 2**2-14**2-15**2 }{ 2 * 14 * 15 } ) = 6° 51'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-2**2-15**2 }{ 2 * 2 * 15 } ) = 56° 37'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-2**2-14**2 }{ 2 * 14 * 2 } ) = 116° 30'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.53 }{ 15.5 } = 0.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 6° 51'8" } = 8.38 ; ;




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