7 25 29 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 25   c = 29

Area: T = 76.89772528768
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 12.24772256437° = 12°14'50″ = 0.21437544117 rad
Angle ∠ B = β = 49.25438111784° = 49°15'14″ = 0.86596411742 rad
Angle ∠ C = γ = 118.4998963178° = 118°29'56″ = 2.06881970677 rad

Height: ha = 21.97106436791
Height: hb = 6.15217802301
Height: hc = 5.30332588191

Median: ma = 26.84767875173
Median: mb = 16.9932645468
Median: mc = 11.25883302492

Inradius: r = 2.52112214058
Circumradius: R = 16.49992890192

Vertex coordinates: A[29; 0] B[0; 0] C[4.56989655172; 5.30332588191]
Centroid: CG[11.19896551724; 1.76877529397]
Coordinates of the circumscribed circle: U[14.5; -7.87325179035]
Coordinates of the inscribed circle: I[5.5; 2.52112214058]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.7532774356° = 167°45'10″ = 0.21437544117 rad
∠ B' = β' = 130.7466188822° = 130°44'46″ = 0.86596411742 rad
∠ C' = γ' = 61.50110368221° = 61°30'4″ = 2.06881970677 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 = 25 ; ; c = 29 ; ;

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

p = a+b+c = 7+25+29 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-7)(30.5-25)(30.5-29) } ; ; T = sqrt{ 5913.19 } = 76.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.9 }{ 7 } = 21.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.9 }{ 25 } = 6.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.9 }{ 29 } = 5.3 ; ;

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**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 12° 14'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-7**2-29**2 }{ 2 * 7 * 29 } ) = 49° 15'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-7**2-25**2 }{ 2 * 25 * 7 } ) = 118° 29'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.9 }{ 30.5 } = 2.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 12° 14'50" } = 16.5 ; ;




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