14 25 29 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 25   c = 29

Area: T = 174.9298556845
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 28.85328340448° = 28°51'10″ = 0.50435769526 rad
Angle ∠ B = β = 59.51099208774° = 59°30'36″ = 1.03986440569 rad
Angle ∠ C = γ = 91.63772450778° = 91°38'14″ = 1.59993716441 rad

Height: ha = 24.99897938351
Height: hb = 13.99442845476
Height: hc = 12.06440384031

Median: ma = 26.15333936612
Median: mb = 19.03328663107
Median: mc = 14.15109716981

Inradius: r = 5.14549575543
Circumradius: R = 14.50659219933

Vertex coordinates: A[29; 0] B[0; 0] C[7.10334482759; 12.06440384031]
Centroid: CG[12.03444827586; 4.02113461344]
Coordinates of the circumscribed circle: U[14.5; -0.41444549141]
Coordinates of the inscribed circle: I[9; 5.14549575543]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.1477165955° = 151°8'50″ = 0.50435769526 rad
∠ B' = β' = 120.4990079123° = 120°29'24″ = 1.03986440569 rad
∠ C' = γ' = 88.36327549222° = 88°21'46″ = 1.59993716441 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 14+25+29 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-14)(34-25)(34-29) } ; ; T = sqrt{ 30600 } = 174.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 174.93 }{ 14 } = 24.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 174.93 }{ 25 } = 13.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 174.93 }{ 29 } = 12.06 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 28° 51'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 59° 30'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-25**2 }{ 2 * 25 * 14 } ) = 91° 38'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 174.93 }{ 34 } = 5.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 51'10" } = 14.51 ; ;




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