15 26 26 triangle

Acute isosceles triangle.

Sides: a = 15   b = 26   c = 26

Area: T = 186.7110839268
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 33.53217459453° = 33°31'54″ = 0.58552393707 rad
Angle ∠ B = β = 73.23441270273° = 73°14'3″ = 1.27881766415 rad
Angle ∠ C = γ = 73.23441270273° = 73°14'3″ = 1.27881766415 rad

Height: ha = 24.8954778569
Height: hb = 14.36223722514
Height: hc = 14.36223722514

Median: ma = 24.8954778569
Median: mb = 16.77879617356
Median: mc = 16.77879617356

Inradius: r = 5.57334578886
Circumradius: R = 13.57771442619

Vertex coordinates: A[26; 0] B[0; 0] C[4.32769230769; 14.36223722514]
Centroid: CG[10.1098974359; 4.78774574171]
Coordinates of the circumscribed circle: U[13; 3.91664839217]
Coordinates of the inscribed circle: I[7.5; 5.57334578886]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4688254055° = 146°28'6″ = 0.58552393707 rad
∠ B' = β' = 106.7665872973° = 106°45'57″ = 1.27881766415 rad
∠ C' = γ' = 106.7665872973° = 106°45'57″ = 1.27881766415 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 = 15 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 15+26+26 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-15)(33.5-26)(33.5-26) } ; ; T = sqrt{ 34860.94 } = 186.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 186.71 }{ 15 } = 24.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 186.71 }{ 26 } = 14.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 186.71 }{ 26 } = 14.36 ; ;

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{ 15**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 33° 31'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 73° 14'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-26**2 }{ 2 * 26 * 15 } ) = 73° 14'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 186.71 }{ 33.5 } = 5.57 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 33° 31'54" } = 13.58 ; ;




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