14 23 25 triangle

Acute scalene triangle.

Sides: a = 14   b = 23   c = 25

Area: T = 159.0477162817
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 33.58773419454° = 33°35'14″ = 0.58662097039 rad
Angle ∠ B = β = 65.34656649255° = 65°20'44″ = 1.14404970049 rad
Angle ∠ C = γ = 81.06769931291° = 81°4'1″ = 1.41548859448 rad

Height: ha = 22.72110232595
Height: hb = 13.8330188071
Height: hc = 12.72437730253

Median: ma = 22.97882505862
Median: mb = 16.68108273176
Median: mc = 14.36114066163

Inradius: r = 5.13105536392
Circumradius: R = 12.65334794105

Vertex coordinates: A[25; 0] B[0; 0] C[5.84; 12.72437730253]
Centroid: CG[10.28; 4.24112576751]
Coordinates of the circumscribed circle: U[12.5; 1.96548259954]
Coordinates of the inscribed circle: I[8; 5.13105536392]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4132658055° = 146°24'46″ = 0.58662097039 rad
∠ B' = β' = 114.6544335075° = 114°39'16″ = 1.14404970049 rad
∠ C' = γ' = 98.93330068709° = 98°55'59″ = 1.41548859448 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 = 14 ; ; b = 23 ; ; c = 25 ; ;

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

p = a+b+c = 14+23+25 = 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 * (31-14)(31-23)(31-25) } ; ; T = sqrt{ 25296 } = 159.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 159.05 }{ 14 } = 22.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 159.05 }{ 23 } = 13.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 159.05 }{ 25 } = 12.72 ; ;

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{ 14**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 33° 35'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 65° 20'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-23**2 }{ 2 * 23 * 14 } ) = 81° 4'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 159.05 }{ 31 } = 5.13 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 33° 35'14" } = 12.65 ; ;




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