11 24 26 triangle

Acute scalene triangle.

Sides: a = 11   b = 24   c = 26

Area: T = 131.896555527
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 25.00878332347° = 25°28″ = 0.43664690287 rad
Angle ∠ B = β = 67.27215774025° = 67°16'18″ = 1.17441105187 rad
Angle ∠ C = γ = 87.72105893628° = 87°43'14″ = 1.53110131062 rad

Height: ha = 23.98110100491
Height: hb = 10.99112962725
Height: hc = 10.14658119439

Median: ma = 24.40879904949
Median: mb = 15.95330561335
Median: mc = 13.3987761007

Inradius: r = 4.32444444351
Circumradius: R = 13.01102943688

Vertex coordinates: A[26; 0] B[0; 0] C[4.25; 10.14658119439]
Centroid: CG[10.08333333333; 3.38219373146]
Coordinates of the circumscribed circle: U[13; 0.51774548897]
Coordinates of the inscribed circle: I[6.5; 4.32444444351]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.9922166765° = 154°59'32″ = 0.43664690287 rad
∠ B' = β' = 112.7288422598° = 112°43'42″ = 1.17441105187 rad
∠ C' = γ' = 92.27994106372° = 92°16'46″ = 1.53110131062 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 = 24 ; ; c = 26 ; ;

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

p = a+b+c = 11+24+26 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-11)(30.5-24)(30.5-26) } ; ; T = sqrt{ 17396.44 } = 131.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.9 }{ 11 } = 23.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.9 }{ 24 } = 10.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.9 }{ 26 } = 10.15 ; ;

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**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 25° 28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-11**2-26**2 }{ 2 * 11 * 26 } ) = 67° 16'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-11**2-24**2 }{ 2 * 24 * 11 } ) = 87° 43'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.9 }{ 30.5 } = 4.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 25° 28" } = 13.01 ; ;




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