17 25 27 triangle

Acute scalene triangle.

Sides: a = 17   b = 25   c = 27

Area: T = 207.4065852135
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 37.91882026564° = 37°55'6″ = 0.66217974828 rad
Angle ∠ B = β = 64.65326682678° = 64°39'10″ = 1.12884019315 rad
Angle ∠ C = γ = 77.42991290757° = 77°25'45″ = 1.35113932393 rad

Height: ha = 24.40106884865
Height: hb = 16.59224681708
Height: hc = 15.36333964545

Median: ma = 24.59216652547
Median: mb = 18.7821639971
Median: mc = 16.57655844543

Inradius: r = 6.012176383
Circumradius: R = 13.83215769322

Vertex coordinates: A[27; 0] B[0; 0] C[7.27877777778; 15.36333964545]
Centroid: CG[11.42659259259; 5.12111321515]
Coordinates of the circumscribed circle: U[13.5; 3.01104020382]
Coordinates of the inscribed circle: I[9.5; 6.012176383]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0821797344° = 142°4'54″ = 0.66217974828 rad
∠ B' = β' = 115.3477331732° = 115°20'50″ = 1.12884019315 rad
∠ C' = γ' = 102.5710870924° = 102°34'15″ = 1.35113932393 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 = 17 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 17+25+27 = 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 * (34.5-17)(34.5-25)(34.5-27) } ; ; T = sqrt{ 43017.19 } = 207.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 207.41 }{ 17 } = 24.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 207.41 }{ 25 } = 16.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 207.41 }{ 27 } = 15.36 ; ;

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{ 17**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 37° 55'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-17**2-27**2 }{ 2 * 17 * 27 } ) = 64° 39'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-17**2-25**2 }{ 2 * 25 * 17 } ) = 77° 25'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 207.41 }{ 34.5 } = 6.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 37° 55'6" } = 13.83 ; ;




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