13 18 30 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 18   c = 30

Area: T = 57.75875752607
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 12.35219946365° = 12°21'7″ = 0.21655829756 rad
Angle ∠ B = β = 17.22990702856° = 17°13'45″ = 0.30107040035 rad
Angle ∠ C = γ = 150.4198935078° = 150°25'8″ = 2.62553056745 rad

Height: ha = 8.88657808093
Height: hb = 6.41875083623
Height: hc = 3.85105050174

Median: ma = 23.86994365246
Median: mb = 21.2965539439
Median: mc = 4.63768092477

Inradius: r = 1.89436909922
Circumradius: R = 30.38656246056

Vertex coordinates: A[30; 0] B[0; 0] C[12.41766666667; 3.85105050174]
Centroid: CG[14.13988888889; 1.28435016725]
Coordinates of the circumscribed circle: U[15; -26.42551051591]
Coordinates of the inscribed circle: I[12.5; 1.89436909922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.6488005363° = 167°38'53″ = 0.21655829756 rad
∠ B' = β' = 162.7710929714° = 162°46'15″ = 0.30107040035 rad
∠ C' = γ' = 29.58110649222° = 29°34'52″ = 2.62553056745 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 = 13 ; ; b = 18 ; ; c = 30 ; ;

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

p = a+b+c = 13+18+30 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-13)(30.5-18)(30.5-30) } ; ; T = sqrt{ 3335.94 } = 57.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.76 }{ 13 } = 8.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.76 }{ 18 } = 6.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.76 }{ 30 } = 3.85 ; ;

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{ 13**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 12° 21'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-13**2-30**2 }{ 2 * 13 * 30 } ) = 17° 13'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-13**2-18**2 }{ 2 * 18 * 13 } ) = 150° 25'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.76 }{ 30.5 } = 1.89 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 12° 21'7" } = 30.39 ; ;




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