15 17 23 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 23

Area: T = 127.445484101
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 40.68443855292° = 40°41'4″ = 0.71100764816 rad
Angle ∠ B = β = 47.63302014306° = 47°37'49″ = 0.83113038384 rad
Angle ∠ C = γ = 91.68554130402° = 91°41'7″ = 1.66002123336 rad

Height: ha = 16.9932645468
Height: hb = 14.9943510707
Height: hc = 11.08221600878

Median: ma = 18.7821639971
Median: mb = 17.45770902501
Median: mc = 11.16991539518

Inradius: r = 4.63443578549
Circumradius: R = 11.50549772779

Vertex coordinates: A[23; 0] B[0; 0] C[10.10986956522; 11.08221600878]
Centroid: CG[11.03662318841; 3.69440533626]
Coordinates of the circumscribed circle: U[11.5; -0.33883816846]
Coordinates of the inscribed circle: I[10.5; 4.63443578549]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.3165614471° = 139°18'56″ = 0.71100764816 rad
∠ B' = β' = 132.3769798569° = 132°22'11″ = 0.83113038384 rad
∠ C' = γ' = 88.31545869598° = 88°18'53″ = 1.66002123336 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 = 23 ; ;

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

p = a+b+c = 15+17+23 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-15)(27.5-17)(27.5-23) } ; ; T = sqrt{ 16242.19 } = 127.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 127.44 }{ 15 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 127.44 }{ 17 } = 14.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 127.44 }{ 23 } = 11.08 ; ;

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**2-23**2 }{ 2 * 17 * 23 } ) = 40° 41'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-23**2 }{ 2 * 15 * 23 } ) = 47° 37'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 91° 41'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 127.44 }{ 27.5 } = 4.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 40° 41'4" } = 11.5 ; ;




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