12 17 25 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 17   c = 25

Area: T = 90
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 25.05876154183° = 25°3'27″ = 0.43773378917 rad
Angle ∠ B = β = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ C = γ = 118.0722486936° = 118°4'21″ = 2.0610753653 rad

Height: ha = 15
Height: hb = 10.58882352941
Height: hc = 7.2

Median: ma = 20.51882845287
Median: mb = 17.67105970471
Median: mc = 7.76220873481

Inradius: r = 3.33333333333
Circumradius: R = 14.16766666667

Vertex coordinates: A[25; 0] B[0; 0] C[9.6; 7.2]
Centroid: CG[11.53333333333; 2.4]
Coordinates of the circumscribed circle: U[12.5; -6.66766666667]
Coordinates of the inscribed circle: I[10; 3.33333333333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.9422384582° = 154°56'33″ = 0.43773378917 rad
∠ B' = β' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ C' = γ' = 61.92875130641° = 61°55'39″ = 2.0610753653 rad

Calculate another triangle




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 = 17 ; ; c = 25 ; ;

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

p = a+b+c = 12+17+25 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-12)(27-17)(27-25) } ; ; T = sqrt{ 8100 } = 90 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 90 }{ 12 } = 15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 90 }{ 17 } = 10.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90 }{ 25 } = 7.2 ; ;

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**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 25° 3'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-12**2-25**2 }{ 2 * 12 * 25 } ) = 36° 52'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-12**2-17**2 }{ 2 * 17 * 12 } ) = 118° 4'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90 }{ 27 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 25° 3'27" } = 14.17 ; ;




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