11 16 26 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 16   c = 26

Area: T = 46.43774579408
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 12.99004051848° = 12°54'1″ = 0.22551545453 rad
Angle ∠ B = β = 18.95496703376° = 18°56'59″ = 0.33107341396 rad
Angle ∠ C = γ = 148.1549924478° = 148°9' = 2.58657039687 rad

Height: ha = 8.4433174171
Height: hb = 5.80546822426
Height: hc = 3.57221121493

Median: ma = 20.87546257451
Median: mb = 18.28993411582
Median: mc = 4.41658804332

Inradius: r = 1.75223569034
Circumradius: R = 24.63552847621

Vertex coordinates: A[26; 0] B[0; 0] C[10.40438461538; 3.57221121493]
Centroid: CG[12.13546153846; 1.19107040498]
Coordinates of the circumscribed circle: U[13; -20.92659947269]
Coordinates of the inscribed circle: I[10.5; 1.75223569034]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.1099594815° = 167°5'59″ = 0.22551545453 rad
∠ B' = β' = 161.0550329662° = 161°3'1″ = 0.33107341396 rad
∠ C' = γ' = 31.85500755224° = 31°51' = 2.58657039687 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 = 16 ; ; c = 26 ; ;

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

p = a+b+c = 11+16+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-11)(26.5-16)(26.5-26) } ; ; T = sqrt{ 2156.44 } = 46.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.44 }{ 11 } = 8.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.44 }{ 16 } = 5.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.44 }{ 26 } = 3.57 ; ;

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**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 12° 54'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-11**2-26**2 }{ 2 * 11 * 26 } ) = 18° 56'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-11**2-16**2 }{ 2 * 16 * 11 } ) = 148° 9' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.44 }{ 26.5 } = 1.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 12° 54'1" } = 24.64 ; ;




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