25 26 30 triangle

Acute scalene triangle.

Sides: a = 25   b = 26   c = 30

Area: T = 309.1521965059
Perimeter: p = 81
Semiperimeter: s = 40.5

Angle ∠ A = α = 52.43883020381° = 52°26'18″ = 0.91552210247 rad
Angle ∠ B = β = 55.52882380553° = 55°31'42″ = 0.96991505819 rad
Angle ∠ C = γ = 72.03334599066° = 72°2' = 1.2577221047 rad

Height: ha = 24.73221572047
Height: hb = 23.78109203892
Height: hc = 20.6110131004

Median: ma = 25.13546374551
Median: mb = 24.36218554302
Median: mc = 20.62876513447

Inradius: r = 7.63333818533
Circumradius: R = 15.76989439207

Vertex coordinates: A[30; 0] B[0; 0] C[14.15; 20.6110131004]
Centroid: CG[14.71766666667; 6.8770043668]
Coordinates of the circumscribed circle: U[15; 4.86441127017]
Coordinates of the inscribed circle: I[14.5; 7.63333818533]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.5621697962° = 127°33'42″ = 0.91552210247 rad
∠ B' = β' = 124.4721761945° = 124°28'18″ = 0.96991505819 rad
∠ C' = γ' = 107.9676540093° = 107°58' = 1.2577221047 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 = 26 ; ; c = 30 ; ;

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

p = a+b+c = 25+26+30 = 81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81 }{ 2 } = 40.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.5 * (40.5-25)(40.5-26)(40.5-30) } ; ; T = sqrt{ 95574.94 } = 309.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 309.15 }{ 25 } = 24.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 309.15 }{ 26 } = 23.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 309.15 }{ 30 } = 20.61 ; ;

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**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 52° 26'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 55° 31'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-25**2-26**2 }{ 2 * 26 * 25 } ) = 72° 2' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 309.15 }{ 40.5 } = 7.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 52° 26'18" } = 15.77 ; ;




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