18 26 28 triangle

Acute scalene triangle.

Sides: a = 18   b = 26   c = 28

Area: T = 227.6843991532
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 38.71992973222° = 38°43'9″ = 0.67657792223 rad
Angle ∠ B = β = 64.62330664748° = 64°37'23″ = 1.12878852827 rad
Angle ∠ C = γ = 76.65876362029° = 76°39'28″ = 1.33879281485 rad

Height: ha = 25.29882212813
Height: hb = 17.51441531948
Height: hc = 16.26331422523

Median: ma = 25.47554784057
Median: mb = 19.62114168703
Median: mc = 17.43655957742

Inradius: r = 6.32545553203
Circumradius: R = 14.38883633538

Vertex coordinates: A[28; 0] B[0; 0] C[7.71442857143; 16.26331422523]
Centroid: CG[11.90547619048; 5.42110474174]
Coordinates of the circumscribed circle: U[14; 3.32203915432]
Coordinates of the inscribed circle: I[10; 6.32545553203]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.2810702678° = 141°16'51″ = 0.67657792223 rad
∠ B' = β' = 115.3776933525° = 115°22'37″ = 1.12878852827 rad
∠ C' = γ' = 103.3422363797° = 103°20'32″ = 1.33879281485 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 = 26 ; ; c = 28 ; ;

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

p = a+b+c = 18+26+28 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-18)(36-26)(36-28) } ; ; T = sqrt{ 51840 } = 227.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 227.68 }{ 18 } = 25.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 227.68 }{ 26 } = 17.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 227.68 }{ 28 } = 16.26 ; ;

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**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 38° 43'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 64° 37'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-18**2-26**2 }{ 2 * 26 * 18 } ) = 76° 39'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 227.68 }{ 36 } = 6.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 38° 43'9" } = 14.39 ; ;




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