5 25 29 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 25   c = 29

Area: T = 40.32660151763
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 6.38770420437° = 6°23'13″ = 0.11114749131 rad
Angle ∠ B = β = 33.79548485051° = 33°47'41″ = 0.59898313766 rad
Angle ∠ C = γ = 139.8188109451° = 139°49'5″ = 2.44402863638 rad

Height: ha = 16.13304060705
Height: hb = 3.22660812141
Height: hc = 2.78111044949

Median: ma = 26.95883011334
Median: mb = 16.63658047596
Median: mc = 10.71221426428

Inradius: r = 1.36769835653
Circumradius: R = 22.47330858241

Vertex coordinates: A[29; 0] B[0; 0] C[4.15551724138; 2.78111044949]
Centroid: CG[11.05217241379; 0.92770348316]
Coordinates of the circumscribed circle: U[14.5; -17.16994375696]
Coordinates of the inscribed circle: I[4.5; 1.36769835653]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.6132957956° = 173°36'47″ = 0.11114749131 rad
∠ B' = β' = 146.2055151495° = 146°12'19″ = 0.59898313766 rad
∠ C' = γ' = 40.18218905488° = 40°10'55″ = 2.44402863638 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 = 5 ; ; b = 25 ; ; c = 29 ; ;

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

p = a+b+c = 5+25+29 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-5)(29.5-25)(29.5-29) } ; ; T = sqrt{ 1626.19 } = 40.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.33 }{ 5 } = 16.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.33 }{ 25 } = 3.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.33 }{ 29 } = 2.78 ; ;

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{ 5**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 6° 23'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-5**2-29**2 }{ 2 * 5 * 29 } ) = 33° 47'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-5**2-25**2 }{ 2 * 25 * 5 } ) = 139° 49'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.33 }{ 29.5 } = 1.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 6° 23'13" } = 22.47 ; ;




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