15 18 30 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 18   c = 30

Area: T = 102.5911118037
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 22.33216450092° = 22°19'54″ = 0.39897607328 rad
Angle ∠ B = β = 27.12767531173° = 27°7'36″ = 0.47334511573 rad
Angle ∠ C = γ = 130.5421601874° = 130°32'30″ = 2.27883807635 rad

Height: ha = 13.67988157382
Height: hb = 11.39990131152
Height: hc = 6.83994078691

Median: ma = 23.57443504683
Median: mb = 21.94331082575
Median: mc = 7.03656236397

Inradius: r = 3.25768608901
Circumradius: R = 19.73985508488

Vertex coordinates: A[30; 0] B[0; 0] C[13.35; 6.83994078691]
Centroid: CG[14.45; 2.2879802623]
Coordinates of the circumscribed circle: U[15; -12.83300580517]
Coordinates of the inscribed circle: I[13.5; 3.25768608901]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.6688354991° = 157°40'6″ = 0.39897607328 rad
∠ B' = β' = 152.8733246883° = 152°52'24″ = 0.47334511573 rad
∠ C' = γ' = 49.45883981265° = 49°27'30″ = 2.27883807635 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 = 30 ; ;

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

p = a+b+c = 15+18+30 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-15)(31.5-18)(31.5-30) } ; ; T = sqrt{ 10524.94 } = 102.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 102.59 }{ 15 } = 13.68 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 102.59 }{ 18 } = 11.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 102.59 }{ 30 } = 6.84 ; ;

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**2-30**2 }{ 2 * 18 * 30 } ) = 22° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-15**2-30**2 }{ 2 * 15 * 30 } ) = 27° 7'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-15**2-18**2 }{ 2 * 18 * 15 } ) = 130° 32'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 102.59 }{ 31.5 } = 3.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 22° 19'54" } = 19.74 ; ;




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