15 18 29 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 18   c = 29

Area: T = 113.5610556533
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 25.79215246995° = 25°47'29″ = 0.45501470251 rad
Angle ∠ B = β = 31.47443967758° = 31°28'28″ = 0.54993318538 rad
Angle ∠ C = γ = 122.7344078525° = 122°44'3″ = 2.14221137747 rad

Height: ha = 15.14114075377
Height: hb = 12.61878396147
Height: hc = 7.83217625195

Median: ma = 22.94401394939
Median: mb = 21.26602916255
Median: mc = 8.01656097709

Inradius: r = 3.66332437591
Circumradius: R = 17.2377499179

Vertex coordinates: A[29; 0] B[0; 0] C[12.79331034483; 7.83217625195]
Centroid: CG[13.93110344828; 2.61105875065]
Coordinates of the circumscribed circle: U[14.5; -9.32110180746]
Coordinates of the inscribed circle: I[13; 3.66332437591]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.20884753° = 154°12'31″ = 0.45501470251 rad
∠ B' = β' = 148.5265603224° = 148°31'32″ = 0.54993318538 rad
∠ C' = γ' = 57.26659214754° = 57°15'57″ = 2.14221137747 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 = 29 ; ;

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

p = a+b+c = 15+18+29 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-15)(31-18)(31-29) } ; ; T = sqrt{ 12896 } = 113.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 113.56 }{ 15 } = 15.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 113.56 }{ 18 } = 12.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 113.56 }{ 29 } = 7.83 ; ;

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**2-29**2 }{ 2 * 18 * 29 } ) = 25° 47'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-15**2-29**2 }{ 2 * 15 * 29 } ) = 31° 28'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-15**2-18**2 }{ 2 * 18 * 15 } ) = 122° 44'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 113.56 }{ 31 } = 3.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 25° 47'29" } = 17.24 ; ;




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