18 23 29 triangle

Acute scalene triangle.

Sides: a = 18   b = 23   c = 29

Area: T = 206.9788259728
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 38.36217507117° = 38°21'42″ = 0.67695388567 rad
Angle ∠ B = β = 52.46986519758° = 52°28'7″ = 0.91657507311 rad
Angle ∠ C = γ = 89.17695973125° = 89°10'11″ = 1.55663030658 rad

Height: ha = 22.99875844142
Height: hb = 17.99881095416
Height: hc = 14.27443627399

Median: ma = 24.57664114549
Median: mb = 21.21990951739
Median: mc = 14.70554411699

Inradius: r = 5.91436645637
Circumradius: R = 14.50215230293

Vertex coordinates: A[29; 0] B[0; 0] C[10.96655172414; 14.27443627399]
Centroid: CG[13.32218390805; 4.75881209133]
Coordinates of the circumscribed circle: U[14.5; 0.21101670004]
Coordinates of the inscribed circle: I[12; 5.91436645637]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.6388249288° = 141°38'18″ = 0.67695388567 rad
∠ B' = β' = 127.5311348024° = 127°31'53″ = 0.91657507311 rad
∠ C' = γ' = 90.83304026875° = 90°49'49″ = 1.55663030658 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 = 18 ; ; b = 23 ; ; c = 29 ; ;

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

p = a+b+c = 18+23+29 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-18)(35-23)(35-29) } ; ; T = sqrt{ 42840 } = 206.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 206.98 }{ 18 } = 23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 206.98 }{ 23 } = 18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 206.98 }{ 29 } = 14.27 ; ;

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{ 18**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 38° 21'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-18**2-29**2 }{ 2 * 18 * 29 } ) = 52° 28'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-18**2-23**2 }{ 2 * 23 * 18 } ) = 89° 10'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 206.98 }{ 35 } = 5.91 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 38° 21'42" } = 14.5 ; ;




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