12 18 25 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 18   c = 25

Area: T = 100.6155294563
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 26.56328406278° = 26°33'46″ = 0.46436090276 rad
Angle ∠ B = β = 42.12664158149° = 42°7'35″ = 0.7355244658 rad
Angle ∠ C = γ = 111.3110743557° = 111°18'39″ = 1.94327389679 rad

Height: ha = 16.76992157605
Height: hb = 11.17994771737
Height: hc = 8.0499223565

Median: ma = 20.94403915914
Median: mb = 17.42112513902
Median: mc = 8.81875960443

Inradius: r = 3.65987379841
Circumradius: R = 13.41774432015

Vertex coordinates: A[25; 0] B[0; 0] C[8.9; 8.0499223565]
Centroid: CG[11.3; 2.68330745217]
Coordinates of the circumscribed circle: U[12.5; -4.87662467191]
Coordinates of the inscribed circle: I[9.5; 3.65987379841]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4377159372° = 153°26'14″ = 0.46436090276 rad
∠ B' = β' = 137.8743584185° = 137°52'25″ = 0.7355244658 rad
∠ C' = γ' = 68.68992564427° = 68°41'21″ = 1.94327389679 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 = 12 ; ; b = 18 ; ; c = 25 ; ;

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

p = a+b+c = 12+18+25 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-12)(27.5-18)(27.5-25) } ; ; T = sqrt{ 10123.44 } = 100.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 100.62 }{ 12 } = 16.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 100.62 }{ 18 } = 11.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 100.62 }{ 25 } = 8.05 ; ;

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{ 12**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 26° 33'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 42° 7'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-18**2 }{ 2 * 18 * 12 } ) = 111° 18'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 100.62 }{ 27.5 } = 3.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 26° 33'46" } = 13.42 ; ;




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