11 25 26 triangle

Acute scalene triangle.

Sides: a = 11   b = 25   c = 26

Area: T = 136.382181697
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 24.81216315026° = 24°48'42″ = 0.43330446625 rad
Angle ∠ B = β = 72.55003904237° = 72°30'1″ = 1.26553705219 rad
Angle ∠ C = γ = 82.68879780737° = 82°41'17″ = 1.44331774692 rad

Height: ha = 24.79766939945
Height: hb = 10.91105453576
Height: hc = 10.49109089977

Median: ma = 24.90548188108
Median: mb = 15.56443824163
Median: mc = 14.28328568571

Inradius: r = 4.39994134506
Circumradius: R = 13.1076585905

Vertex coordinates: A[26; 0] B[0; 0] C[3.30876923077; 10.49109089977]
Centroid: CG[9.76992307692; 3.49769696659]
Coordinates of the circumscribed circle: U[13; 1.66881109334]
Coordinates of the inscribed circle: I[6; 4.39994134506]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1888368497° = 155°11'18″ = 0.43330446625 rad
∠ B' = β' = 107.5499609576° = 107°29'59″ = 1.26553705219 rad
∠ C' = γ' = 97.31220219263° = 97°18'43″ = 1.44331774692 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 = 25 ; ; c = 26 ; ;

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

p = a+b+c = 11+25+26 = 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 * (31-11)(31-25)(31-26) } ; ; T = sqrt{ 18600 } = 136.38 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 136.38 }{ 11 } = 24.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 136.38 }{ 25 } = 10.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 136.38 }{ 26 } = 10.49 ; ;

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**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 24° 48'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-11**2-26**2 }{ 2 * 11 * 26 } ) = 72° 30'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-11**2-25**2 }{ 2 * 25 * 11 } ) = 82° 41'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 136.38 }{ 31 } = 4.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 48'42" } = 13.11 ; ;




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