15.23 7.62 17.03 triangle

Obtuse scalene triangle.

Sides: a = 15.23   b = 7.62   c = 17.03

Area: T = 58.0266299993
Perimeter: p = 39.88
Semiperimeter: s = 19.94

Angle ∠ A = α = 63.41991919155° = 63°25'9″ = 1.10768737079 rad
Angle ∠ B = β = 26.5879919415° = 26°34'48″ = 0.46439071087 rad
Angle ∠ C = γ = 90.00108886695° = 90°3″ = 1.5710811837 rad

Height: ha = 7.62199999991
Height: hb = 15.23299999982
Height: hc = 6.81545977678

Median: ma = 10.77328559352
Median: mb = 15.69993885231
Median: mc = 8.51548943035

Inradius: r = 2.91100451351
Circumradius: R = 8.5155000001

Vertex coordinates: A[17.03; 0] B[0; 0] C[13.62203581914; 6.81545977678]
Centroid: CG[10.21767860638; 2.27215325893]
Coordinates of the circumscribed circle: U[8.515; -00.0001320694]
Coordinates of the inscribed circle: I[12.32; 2.91100451351]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5810808085° = 116°34'51″ = 1.10768737079 rad
∠ B' = β' = 153.4220080585° = 153°25'12″ = 0.46439071087 rad
∠ C' = γ' = 89.99991113305° = 89°59'57″ = 1.5710811837 rad

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How did we calculate this triangle?

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

p = a+b+c = 15.23+7.62+17.03 = 39.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39.88 }{ 2 } = 19.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.94 * (19.94-15.23)(19.94-7.62)(19.94-17.03) } ; ; T = sqrt{ 3367.05 } = 58.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 58.03 }{ 15.23 } = 7.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 58.03 }{ 7.62 } = 15.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 58.03 }{ 17.03 } = 6.81 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 7.62**2+17.03**2-15.23**2 }{ 2 * 7.62 * 17.03 } ) = 63° 25'9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15.23**2+17.03**2-7.62**2 }{ 2 * 15.23 * 17.03 } ) = 26° 34'48" ; ;
 gamma = 180° - alpha - beta = 180° - 63° 25'9" - 26° 34'48" = 90° 3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 58.03 }{ 19.94 } = 2.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15.23 }{ 2 * sin 63° 25'9" } = 8.52 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.62**2+2 * 17.03**2 - 15.23**2 } }{ 2 } = 10.773 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.03**2+2 * 15.23**2 - 7.62**2 } }{ 2 } = 15.699 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.62**2+2 * 15.23**2 - 17.03**2 } }{ 2 } = 8.515 ; ;
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