18 24 26 triangle

Acute scalene triangle.

Sides: a = 18   b = 24   c = 26

Area: T = 208.6144476967
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 41.96218888284° = 41°57'43″ = 0.73223731204 rad
Angle ∠ B = β = 63.06442249308° = 63°3'51″ = 1.10106783653 rad
Angle ∠ C = γ = 74.97438862409° = 74°58'26″ = 1.30985411679 rad

Height: ha = 23.17993863296
Height: hb = 17.38545397472
Height: hc = 16.0477267459

Median: ma = 23.34552350599
Median: mb = 18.86879622641
Median: mc = 16.76330546142

Inradius: r = 6.13657199108
Circumradius: R = 13.46602355543

Vertex coordinates: A[26; 0] B[0; 0] C[8.15438461538; 16.0477267459]
Centroid: CG[11.38546153846; 5.3499089153]
Coordinates of the circumscribed circle: U[13; 3.49896906993]
Coordinates of the inscribed circle: I[10; 6.13657199108]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0388111172° = 138°2'17″ = 0.73223731204 rad
∠ B' = β' = 116.9365775069° = 116°56'9″ = 1.10106783653 rad
∠ C' = γ' = 105.0266113759° = 105°1'34″ = 1.30985411679 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 = 18 ; ; b = 24 ; ; c = 26 ; ;

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

p = a+b+c = 18+24+26 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-18)(34-24)(34-26) } ; ; T = sqrt{ 43520 } = 208.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 208.61 }{ 18 } = 23.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 208.61 }{ 24 } = 17.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 208.61 }{ 26 } = 16.05 ; ;

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{ 18**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 41° 57'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 63° 3'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-18**2-24**2 }{ 2 * 24 * 18 } ) = 74° 58'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 208.61 }{ 34 } = 6.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 41° 57'43" } = 13.46 ; ;




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