9 24 29 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 24   c = 29

Area: T = 97.71438680024
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 16.3077179561° = 16°18'26″ = 0.28546139751 rad
Angle ∠ B = β = 48.48435348519° = 48°29'1″ = 0.84661973162 rad
Angle ∠ C = γ = 115.2099285587° = 115°12'33″ = 2.01107813624 rad

Height: ha = 21.71441928894
Height: hb = 8.14328223335
Height: hc = 6.73988874484

Median: ma = 26.23545192447
Median: mb = 17.80444938148
Median: mc = 10.87442815855

Inradius: r = 3.15220602581
Circumradius: R = 16.02663842995

Vertex coordinates: A[29; 0] B[0; 0] C[5.96655172414; 6.73988874484]
Centroid: CG[11.65551724138; 2.24662958161]
Coordinates of the circumscribed circle: U[14.5; -6.8266052572]
Coordinates of the inscribed circle: I[7; 3.15220602581]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.6932820439° = 163°41'34″ = 0.28546139751 rad
∠ B' = β' = 131.5166465148° = 131°30'59″ = 0.84661973162 rad
∠ C' = γ' = 64.79107144129° = 64°47'27″ = 2.01107813624 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 = 9 ; ; b = 24 ; ; c = 29 ; ;

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

p = a+b+c = 9+24+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 * (31-9)(31-24)(31-29) } ; ; T = sqrt{ 9548 } = 97.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.71 }{ 9 } = 21.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.71 }{ 24 } = 8.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.71 }{ 29 } = 6.74 ; ;

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{ 9**2-24**2-29**2 }{ 2 * 24 * 29 } ) = 16° 18'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-9**2-29**2 }{ 2 * 9 * 29 } ) = 48° 29'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-9**2-24**2 }{ 2 * 24 * 9 } ) = 115° 12'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.71 }{ 31 } = 3.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 16° 18'26" } = 16.03 ; ;




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