25 29 30 triangle

Acute scalene triangle.

Sides: a = 25   b = 29   c = 30

Area: T = 333.7422415644
Perimeter: p = 84
Semiperimeter: s = 42

Angle ∠ A = α = 50.1055251744° = 50°6'19″ = 0.87545016155 rad
Angle ∠ B = β = 62.87107055354° = 62°52'15″ = 1.09773008146 rad
Angle ∠ C = γ = 67.02440427206° = 67°1'27″ = 1.17697902235 rad

Height: ha = 26.69993932515
Height: hb = 23.01767183203
Height: hc = 22.24994943763

Median: ma = 26.72554560298
Median: mb = 23.5
Median: mc = 22.53988553392

Inradius: r = 7.94662479915
Circumradius: R = 16.29325050731

Vertex coordinates: A[30; 0] B[0; 0] C[11.4; 22.24994943763]
Centroid: CG[13.8; 7.41664981254]
Coordinates of the circumscribed circle: U[15; 6.36596950837]
Coordinates of the inscribed circle: I[13; 7.94662479915]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 129.8954748256° = 129°53'41″ = 0.87545016155 rad
∠ B' = β' = 117.1299294465° = 117°7'45″ = 1.09773008146 rad
∠ C' = γ' = 112.9765957279° = 112°58'33″ = 1.17697902235 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 25+29+30 = 84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 84 }{ 2 } = 42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42 * (42-25)(42-29)(42-30) } ; ; T = sqrt{ 111384 } = 333.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 333.74 }{ 25 } = 26.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 333.74 }{ 29 } = 23.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 333.74 }{ 30 } = 22.25 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 50° 6'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 62° 52'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-25**2-29**2 }{ 2 * 29 * 25 } ) = 67° 1'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 333.74 }{ 42 } = 7.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 50° 6'19" } = 16.29 ; ;




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