14 15 17 triangle

Acute scalene triangle.

Sides: a = 14   b = 15   c = 17

Area: T = 99.6799486355
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 51.42656685955° = 51°25'32″ = 0.8987547237 rad
Angle ∠ B = β = 56.89220298157° = 56°53'31″ = 0.99329532384 rad
Angle ∠ C = γ = 71.68223015888° = 71°40'56″ = 1.25110921781 rad

Height: ha = 14.24399266221
Height: hb = 13.29105981807
Height: hc = 11.72769983947

Median: ma = 14.42222051019
Median: mb = 13.6477344064
Median: mc = 11.75879760163

Inradius: r = 4.33438907111
Circumradius: R = 8.95436978233

Vertex coordinates: A[17; 0] B[0; 0] C[7.64770588235; 11.72769983947]
Centroid: CG[8.21656862745; 3.90989994649]
Coordinates of the circumscribed circle: U[8.5; 2.81440193159]
Coordinates of the inscribed circle: I[8; 4.33438907111]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.5744331405° = 128°34'28″ = 0.8987547237 rad
∠ B' = β' = 123.1087970184° = 123°6'29″ = 0.99329532384 rad
∠ C' = γ' = 108.3187698411° = 108°19'4″ = 1.25110921781 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 = 14 ; ; b = 15 ; ; c = 17 ; ;

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

p = a+b+c = 14+15+17 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-14)(23-15)(23-17) } ; ; T = sqrt{ 9936 } = 99.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 99.68 }{ 14 } = 14.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 99.68 }{ 15 } = 13.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 99.68 }{ 17 } = 11.73 ; ;

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{ 14**2-15**2-17**2 }{ 2 * 15 * 17 } ) = 51° 25'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-17**2 }{ 2 * 14 * 17 } ) = 56° 53'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 71° 40'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 99.68 }{ 23 } = 4.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 51° 25'32" } = 8.95 ; ;




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