15 18 25 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 18   c = 25

Area: T = 133.6566275573
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 36.44333636683° = 36°26'36″ = 0.63660566865 rad
Angle ∠ B = β = 45.46659243544° = 45°27'57″ = 0.79435300774 rad
Angle ∠ C = γ = 98.09107119773° = 98°5'27″ = 1.71220058896 rad

Height: ha = 17.8210836743
Height: hb = 14.85106972859
Height: hc = 10.69325020458

Median: ma = 20.45111613362
Median: mb = 18.5477236991
Median: mc = 10.87442815855

Inradius: r = 4.60988370887
Circumradius: R = 12.62656697844

Vertex coordinates: A[25; 0] B[0; 0] C[10.52; 10.69325020458]
Centroid: CG[11.84; 3.56441673486]
Coordinates of the circumscribed circle: U[12.5; -1.77769461178]
Coordinates of the inscribed circle: I[11; 4.60988370887]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.5576636332° = 143°33'24″ = 0.63660566865 rad
∠ B' = β' = 134.5344075646° = 134°32'3″ = 0.79435300774 rad
∠ C' = γ' = 81.90992880227° = 81°54'33″ = 1.71220058896 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 = 15 ; ; b = 18 ; ; c = 25 ; ;

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

p = a+b+c = 15+18+25 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-15)(29-18)(29-25) } ; ; T = sqrt{ 17864 } = 133.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 133.66 }{ 15 } = 17.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 133.66 }{ 18 } = 14.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 133.66 }{ 25 } = 10.69 ; ;

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{ 15**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 36° 26'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-15**2-25**2 }{ 2 * 15 * 25 } ) = 45° 27'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-15**2-18**2 }{ 2 * 18 * 15 } ) = 98° 5'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 133.66 }{ 29 } = 4.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 36° 26'36" } = 12.63 ; ;




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