10 23 29 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 23   c = 29

Area: T = 102.0598806577
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 17.82197451748° = 17°49'11″ = 0.31110132252 rad
Angle ∠ B = β = 44.7377021623° = 44°44'13″ = 0.78108083249 rad
Angle ∠ C = γ = 117.4433233202° = 117°26'36″ = 2.05497711036 rad

Height: ha = 20.41217613155
Height: hb = 8.87546788328
Height: hc = 7.03985383846

Median: ma = 25.69904651573
Median: mb = 18.39215741577
Median: mc = 10.21102889283

Inradius: r = 3.2922219567
Circumradius: R = 16.33986194286

Vertex coordinates: A[29; 0] B[0; 0] C[7.10334482759; 7.03985383846]
Centroid: CG[12.03444827586; 2.34661794615]
Coordinates of the circumscribed circle: U[14.5; -7.53299724323]
Coordinates of the inscribed circle: I[8; 3.2922219567]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.1880254825° = 162°10'49″ = 0.31110132252 rad
∠ B' = β' = 135.2632978377° = 135°15'47″ = 0.78108083249 rad
∠ C' = γ' = 62.55767667978° = 62°33'24″ = 2.05497711036 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 = 10 ; ; b = 23 ; ; c = 29 ; ;

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

p = a+b+c = 10+23+29 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-10)(31-23)(31-29) } ; ; T = sqrt{ 10416 } = 102.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 102.06 }{ 10 } = 20.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 102.06 }{ 23 } = 8.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 102.06 }{ 29 } = 7.04 ; ;

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{ 10**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 17° 49'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-10**2-29**2 }{ 2 * 10 * 29 } ) = 44° 44'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-10**2-23**2 }{ 2 * 23 * 10 } ) = 117° 26'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 102.06 }{ 31 } = 3.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 17° 49'11" } = 16.34 ; ;




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