23 25 29 triangle

Acute scalene triangle.

Sides: a = 23   b = 25   c = 29

Area: T = 276.6466322043
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 49.74437751503° = 49°44'38″ = 0.86881926587 rad
Angle ∠ B = β = 56.05498932346° = 56°3' = 0.97882551823 rad
Angle ∠ C = γ = 74.20663316151° = 74°12'23″ = 1.29551448125 rad

Height: ha = 24.05662019168
Height: hb = 22.13217057635
Height: hc = 19.07990566926

Median: ma = 24.51102019576
Median: mb = 22.99545645751
Median: mc = 19.15107180022

Inradius: r = 7.18656187544
Circumradius: R = 15.06988791711

Vertex coordinates: A[29; 0] B[0; 0] C[12.84548275862; 19.07990566926]
Centroid: CG[13.94882758621; 6.36596855642]
Coordinates of the circumscribed circle: U[14.5; 4.10113558092]
Coordinates of the inscribed circle: I[13.5; 7.18656187544]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.256622485° = 130°15'22″ = 0.86881926587 rad
∠ B' = β' = 123.9550106765° = 123°57' = 0.97882551823 rad
∠ C' = γ' = 105.7943668385° = 105°47'37″ = 1.29551448125 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 = 23 ; ; b = 25 ; ; c = 29 ; ;

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

p = a+b+c = 23+25+29 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-23)(38.5-25)(38.5-29) } ; ; T = sqrt{ 76533.19 } = 276.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 276.65 }{ 23 } = 24.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 276.65 }{ 25 } = 22.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 276.65 }{ 29 } = 19.08 ; ;

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{ 23**2-25**2-29**2 }{ 2 * 25 * 29 } ) = 49° 44'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 56° 3' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-23**2-25**2 }{ 2 * 25 * 23 } ) = 74° 12'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 276.65 }{ 38.5 } = 7.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 49° 44'38" } = 15.07 ; ;




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