9 26 27 triangle

Acute scalene triangle.

Sides: a = 9   b = 26   c = 27

Area: T = 116.7990410565
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 19.43549368501° = 19°26'6″ = 0.3399203638 rad
Angle ∠ B = β = 73.99550641403° = 73°59'42″ = 1.29114574995 rad
Angle ∠ C = γ = 86.57699990096° = 86°34'12″ = 1.51109315162 rad

Height: ha = 25.95334245701
Height: hb = 8.98438777358
Height: hc = 8.65111415234

Median: ma = 26.12199157732
Median: mb = 15.36222914957
Median: mc = 14.00989257261

Inradius: r = 3.76774325989
Circumradius: R = 13.52442267953

Vertex coordinates: A[27; 0] B[0; 0] C[2.48114814815; 8.65111415234]
Centroid: CG[9.82771604938; 2.88437138411]
Coordinates of the circumscribed circle: U[13.5; 0.80991417741]
Coordinates of the inscribed circle: I[5; 3.76774325989]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.565506315° = 160°33'54″ = 0.3399203638 rad
∠ B' = β' = 106.005493586° = 106°18″ = 1.29114574995 rad
∠ C' = γ' = 93.43300009904° = 93°25'48″ = 1.51109315162 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 = 9 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 9+26+27 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-9)(31-26)(31-27) } ; ; T = sqrt{ 13640 } = 116.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 116.79 }{ 9 } = 25.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 116.79 }{ 26 } = 8.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 116.79 }{ 27 } = 8.65 ; ;

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{ 9**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 19° 26'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-9**2-27**2 }{ 2 * 9 * 27 } ) = 73° 59'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-9**2-26**2 }{ 2 * 26 * 9 } ) = 86° 34'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 116.79 }{ 31 } = 3.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 19° 26'6" } = 13.52 ; ;




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