25 27 30 triangle

Acute scalene triangle.

Sides: a = 25   b = 27   c = 30

Area: T = 317.8432728405
Perimeter: p = 82
Semiperimeter: s = 41

Angle ∠ A = α = 51.70218942226° = 51°42'7″ = 0.90223682837 rad
Angle ∠ B = β = 57.94994901188° = 57°56'58″ = 1.01114094024 rad
Angle ∠ C = γ = 70.34986156587° = 70°20'55″ = 1.22878149675 rad

Height: ha = 25.42774182724
Height: hb = 23.54439058078
Height: hc = 21.1989515227

Median: ma = 25.65663832213
Median: mb = 24.08883789409
Median: mc = 21.26602916255

Inradius: r = 7.75222616684
Circumradius: R = 15.92876885943

Vertex coordinates: A[30; 0] B[0; 0] C[13.26766666667; 21.1989515227]
Centroid: CG[14.42222222222; 7.06331717423]
Coordinates of the circumscribed circle: U[15; 5.35664226828]
Coordinates of the inscribed circle: I[14; 7.75222616684]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.2988105777° = 128°17'53″ = 0.90223682837 rad
∠ B' = β' = 122.0510509881° = 122°3'2″ = 1.01114094024 rad
∠ C' = γ' = 109.6511384341° = 109°39'5″ = 1.22878149675 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 = 25 ; ; b = 27 ; ; c = 30 ; ;

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

p = a+b+c = 25+27+30 = 82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 82 }{ 2 } = 41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41 * (41-25)(41-27)(41-30) } ; ; T = sqrt{ 101024 } = 317.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 317.84 }{ 25 } = 25.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 317.84 }{ 27 } = 23.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 317.84 }{ 30 } = 21.19 ; ;

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{ 25**2-27**2-30**2 }{ 2 * 27 * 30 } ) = 51° 42'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 57° 56'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-25**2-27**2 }{ 2 * 27 * 25 } ) = 70° 20'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 317.84 }{ 41 } = 7.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 51° 42'7" } = 15.93 ; ;




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