17 23 25 triangle

Acute scalene triangle.

Sides: a = 17   b = 23   c = 25

Area: T = 189.4522335694
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 41.22109585277° = 41°13'15″ = 0.71994414471 rad
Angle ∠ B = β = 63.06774560504° = 63°4'3″ = 1.10107347589 rad
Angle ∠ C = γ = 75.71215854218° = 75°42'42″ = 1.32114164475 rad

Height: ha = 22.28985100817
Height: hb = 16.47441161473
Height: hc = 15.15661868555

Median: ma = 22.46766419387
Median: mb = 18.02108212909
Median: mc = 15.89881130956

Inradius: r = 5.82993026367
Circumradius: R = 12.89990228125

Vertex coordinates: A[25; 0] B[0; 0] C[7.7; 15.15661868555]
Centroid: CG[10.9; 5.05220622852]
Coordinates of the circumscribed circle: U[12.5; 3.18435184179]
Coordinates of the inscribed circle: I[9.5; 5.82993026367]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.7799041472° = 138°46'45″ = 0.71994414471 rad
∠ B' = β' = 116.933254395° = 116°55'57″ = 1.10107347589 rad
∠ C' = γ' = 104.2888414578° = 104°17'18″ = 1.32114164475 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 = 17 ; ; b = 23 ; ; c = 25 ; ;

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

p = a+b+c = 17+23+25 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-17)(32.5-23)(32.5-25) } ; ; T = sqrt{ 35892.19 } = 189.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 189.45 }{ 17 } = 22.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 189.45 }{ 23 } = 16.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 189.45 }{ 25 } = 15.16 ; ;

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{ 17**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 41° 13'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 63° 4'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 75° 42'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 189.45 }{ 32.5 } = 5.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 41° 13'15" } = 12.9 ; ;




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