10 22 25 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 22   c = 25

Area: T = 109.5211402018
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 23.46994253965° = 23°28'10″ = 0.41096187467 rad
Angle ∠ B = β = 61.18438931672° = 61°11'2″ = 1.0687860385 rad
Angle ∠ C = γ = 95.34766814363° = 95°20'48″ = 1.66441135219 rad

Height: ha = 21.90442804036
Height: hb = 9.95664910926
Height: hc = 8.76217121614

Median: ma = 23.0110866998
Median: mb = 15.54402702679
Median: mc = 11.65111801977

Inradius: r = 3.84328562112
Circumradius: R = 12.55546237965

Vertex coordinates: A[25; 0] B[0; 0] C[4.82; 8.76217121614]
Centroid: CG[9.94; 2.92105707205]
Coordinates of the circumscribed circle: U[12.5; -1.17698626719]
Coordinates of the inscribed circle: I[6.5; 3.84328562112]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.5310574603° = 156°31'50″ = 0.41096187467 rad
∠ B' = β' = 118.8166106833° = 118°48'58″ = 1.0687860385 rad
∠ C' = γ' = 84.65333185637° = 84°39'12″ = 1.66441135219 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 = 10 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 10+22+25 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-10)(28.5-22)(28.5-25) } ; ; T = sqrt{ 11994.94 } = 109.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 109.52 }{ 10 } = 21.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 109.52 }{ 22 } = 9.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 109.52 }{ 25 } = 8.76 ; ;

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{ 10**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 23° 28'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 61° 11'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-22**2 }{ 2 * 22 * 10 } ) = 95° 20'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 109.52 }{ 28.5 } = 3.84 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 23° 28'10" } = 12.55 ; ;




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