7 14 17 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 14   c = 17

Area: T = 47.74993455453
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 23.65766583467° = 23°39'24″ = 0.41328865782 rad
Angle ∠ B = β = 53.37704635026° = 53°22'14″ = 0.93114903114 rad
Angle ∠ C = γ = 102.9732878151° = 102°58'22″ = 1.7977215764 rad

Height: ha = 13.64326701558
Height: hb = 6.82113350779
Height: hc = 5.61875700641

Median: ma = 15.17439909055
Median: mb = 10.95444511501
Median: mc = 7.08987234394

Inradius: r = 2.51331234498
Circumradius: R = 8.72326326402

Vertex coordinates: A[17; 0] B[0; 0] C[4.17664705882; 5.61875700641]
Centroid: CG[7.05988235294; 1.87325233547]
Coordinates of the circumscribed circle: U[8.5; -1.95881420213]
Coordinates of the inscribed circle: I[5; 2.51331234498]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.3433341653° = 156°20'36″ = 0.41328865782 rad
∠ B' = β' = 126.6329536497° = 126°37'46″ = 0.93114903114 rad
∠ C' = γ' = 77.02771218492° = 77°1'38″ = 1.7977215764 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 = 14 ; ; c = 17 ; ;

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

p = a+b+c = 7+14+17 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-7)(19-14)(19-17) } ; ; T = sqrt{ 2280 } = 47.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 47.75 }{ 7 } = 13.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 47.75 }{ 14 } = 6.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 47.75 }{ 17 } = 5.62 ; ;

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**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 23° 39'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-7**2-17**2 }{ 2 * 7 * 17 } ) = 53° 22'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-7**2-14**2 }{ 2 * 14 * 7 } ) = 102° 58'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 47.75 }{ 19 } = 2.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 23° 39'24" } = 8.72 ; ;




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