15 17 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 29

Area: T = 97.84326670732
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 23.38662513464° = 23°23'10″ = 0.40881670857 rad
Angle ∠ B = β = 26.73441466638° = 26°44'3″ = 0.4676598882 rad
Angle ∠ C = γ = 129.887960199° = 129°52'47″ = 2.26768266859 rad

Height: ha = 13.04656889431
Height: hb = 11.51109020086
Height: hc = 6.7487770143

Median: ma = 22.55554871373
Median: mb = 21.46550879337
Median: mc = 6.83773971656

Inradius: r = 3.20879562975
Circumradius: R = 18.895513088

Vertex coordinates: A[29; 0] B[0; 0] C[13.39765517241; 6.7487770143]
Centroid: CG[14.1322183908; 2.24992567143]
Coordinates of the circumscribed circle: U[14.5; -12.1155113329]
Coordinates of the inscribed circle: I[13.5; 3.20879562975]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.6143748654° = 156°36'50″ = 0.40881670857 rad
∠ B' = β' = 153.2665853336° = 153°15'57″ = 0.4676598882 rad
∠ C' = γ' = 50.12203980102° = 50°7'13″ = 2.26768266859 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 = 15 ; ; b = 17 ; ; c = 29 ; ;

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

p = a+b+c = 15+17+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 * (30.5-15)(30.5-17)(30.5-29) } ; ; T = sqrt{ 9573.19 } = 97.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.84 }{ 15 } = 13.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.84 }{ 17 } = 11.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.84 }{ 29 } = 6.75 ; ;

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{ 15**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 23° 23'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 26° 44'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 129° 52'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.84 }{ 30.5 } = 3.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 23° 23'10" } = 18.9 ; ;




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