11 23 25 triangle

Acute scalene triangle.

Sides: a = 11   b = 23   c = 25

Area: T = 126.3465508428
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 26.0769600358° = 26°4'11″ = 0.45550003609 rad
Angle ∠ B = β = 66.76223717562° = 66°45'45″ = 1.16552232036 rad
Angle ∠ C = γ = 87.16880278858° = 87°10'5″ = 1.52113690891 rad

Height: ha = 22.97219106233
Height: hb = 10.98765659503
Height: hc = 10.10876406743

Median: ma = 23.38326859022
Median: mb = 15.51661206492
Median: mc = 12.99903810568

Inradius: r = 4.28328985908
Circumradius: R = 12.51552846324

Vertex coordinates: A[25; 0] B[0; 0] C[4.34; 10.10876406743]
Centroid: CG[9.78; 3.36992135581]
Coordinates of the circumscribed circle: U[12.5; 0.61883441024]
Coordinates of the inscribed circle: I[6.5; 4.28328985908]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.9330399642° = 153°55'49″ = 0.45550003609 rad
∠ B' = β' = 113.2387628244° = 113°14'15″ = 1.16552232036 rad
∠ C' = γ' = 92.83219721142° = 92°49'55″ = 1.52113690891 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 = 11 ; ; b = 23 ; ; c = 25 ; ;

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

p = a+b+c = 11+23+25 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-11)(29.5-23)(29.5-25) } ; ; T = sqrt{ 15963.19 } = 126.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 126.35 }{ 11 } = 22.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 126.35 }{ 23 } = 10.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 126.35 }{ 25 } = 10.11 ; ;

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{ 11**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 26° 4'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 66° 45'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-23**2 }{ 2 * 23 * 11 } ) = 87° 10'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 126.35 }{ 29.5 } = 4.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 26° 4'11" } = 12.52 ; ;




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