17 25 29 triangle

Acute scalene triangle.

Sides: a = 17   b = 25   c = 29

Area: T = 211.7154873119
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 35.73552719822° = 35°44'7″ = 0.62436981552 rad
Angle ∠ B = β = 59.19114935362° = 59°11'29″ = 1.03330864514 rad
Angle ∠ C = γ = 85.07332344816° = 85°4'24″ = 1.4854808047 rad

Height: ha = 24.90876321317
Height: hb = 16.93771898496
Height: hc = 14.60110257324

Median: ma = 25.70550578681
Median: mb = 20.21875666192
Median: mc = 15.70882780724

Inradius: r = 5.96437992428
Circumradius: R = 14.55437720359

Vertex coordinates: A[29; 0] B[0; 0] C[8.70768965517; 14.60110257324]
Centroid: CG[12.56989655172; 4.86770085775]
Coordinates of the circumscribed circle: U[14.5; 1.25499121866]
Coordinates of the inscribed circle: I[10.5; 5.96437992428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.2654728018° = 144°15'53″ = 0.62436981552 rad
∠ B' = β' = 120.8098506464° = 120°48'31″ = 1.03330864514 rad
∠ C' = γ' = 94.92767655184° = 94°55'36″ = 1.4854808047 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 = 17 ; ; b = 25 ; ; c = 29 ; ;

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

p = a+b+c = 17+25+29 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-17)(35.5-25)(35.5-29) } ; ; T = sqrt{ 44823.19 } = 211.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 211.71 }{ 17 } = 24.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 211.71 }{ 25 } = 16.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 211.71 }{ 29 } = 14.6 ; ;

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{ 17**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 35° 44'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 59° 11'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-25**2 }{ 2 * 25 * 17 } ) = 85° 4'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 211.71 }{ 35.5 } = 5.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 35° 44'7" } = 14.55 ; ;




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