18 25 26 triangle

Acute scalene triangle.

Sides: a = 18   b = 25   c = 26

Area: T = 214.399901469
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 41.27661795162° = 41°16'34″ = 0.72204052352 rad
Angle ∠ B = β = 66.38217417975° = 66°22'54″ = 1.15985799576 rad
Angle ∠ C = γ = 72.34220786863° = 72°20'31″ = 1.26326074608 rad

Height: ha = 23.82221127433
Height: hb = 17.15219211752
Height: hc = 16.49222318992

Median: ma = 23.86441991276
Median: mb = 18.54404962177
Median: mc = 17.47985582929

Inradius: r = 6.21444641939
Circumradius: R = 13.64327865782

Vertex coordinates: A[26; 0] B[0; 0] C[7.21215384615; 16.49222318992]
Centroid: CG[11.07105128205; 5.49774106331]
Coordinates of the circumscribed circle: U[13; 4.13883119287]
Coordinates of the inscribed circle: I[9.5; 6.21444641939]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.7243820484° = 138°43'26″ = 0.72204052352 rad
∠ B' = β' = 113.6188258203° = 113°37'6″ = 1.15985799576 rad
∠ C' = γ' = 107.6587921314° = 107°39'29″ = 1.26326074608 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 = 25 ; ; c = 26 ; ;

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

p = a+b+c = 18+25+26 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-18)(34.5-25)(34.5-26) } ; ; T = sqrt{ 45966.94 } = 214.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 214.4 }{ 18 } = 23.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 214.4 }{ 25 } = 17.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 214.4 }{ 26 } = 16.49 ; ;

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**2-25**2-26**2 }{ 2 * 25 * 26 } ) = 41° 16'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 66° 22'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-18**2-25**2 }{ 2 * 25 * 18 } ) = 72° 20'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 214.4 }{ 34.5 } = 6.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 41° 16'34" } = 13.64 ; ;




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