6 24 26 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 24   c = 26

Area: T = 70.21997150991
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 13.00328244668° = 13°10″ = 0.2276942099 rad
Angle ∠ B = β = 64.15875871263° = 64°9'27″ = 1.12197611355 rad
Angle ∠ C = γ = 102.8439588407° = 102°50'23″ = 1.79548894191 rad

Height: ha = 23.4399905033
Height: hb = 5.85499762583
Height: hc = 5.43999780845

Median: ma = 24.83994846967
Median: mb = 14.56602197786
Median: mc = 11.70546999107

Inradius: r = 2.50771326821
Circumradius: R = 13.33333874458

Vertex coordinates: A[26; 0] B[0; 0] C[2.61553846154; 5.43999780845]
Centroid: CG[9.53884615385; 1.87999926948]
Coordinates of the circumscribed circle: U[13; -2.9632974988]
Coordinates of the inscribed circle: I[4; 2.50771326821]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.9977175533° = 166°59'50″ = 0.2276942099 rad
∠ B' = β' = 115.8422412874° = 115°50'33″ = 1.12197611355 rad
∠ C' = γ' = 77.16604115931° = 77°9'37″ = 1.79548894191 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 = 6 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 6+24+26 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-6)(28-24)(28-26) } ; ; T = sqrt{ 4928 } = 70.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.2 }{ 6 } = 23.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.2 }{ 24 } = 5.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.2 }{ 26 } = 5.4 ; ;

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{ 6**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 13° 10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-6**2-26**2 }{ 2 * 6 * 26 } ) = 64° 9'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-6**2-24**2 }{ 2 * 24 * 6 } ) = 102° 50'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.2 }{ 28 } = 2.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 13° 10" } = 13.33 ; ;




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