16 18 30 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 18   c = 30

Area: T = 119.7333036377
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 26.32545765375° = 26°19'28″ = 0.45994505348 rad
Angle ∠ B = β = 29.92664348666° = 29°55'35″ = 0.52223148218 rad
Angle ∠ C = γ = 123.7498988596° = 123°44'56″ = 2.1659827297 rad

Height: ha = 14.96766295471
Height: hb = 13.30436707085
Height: hc = 7.98222024251

Median: ma = 23.40993998214
Median: mb = 22.29334968096
Median: mc = 8.06222577483

Inradius: r = 3.74216573868
Circumradius: R = 18.04401338291

Vertex coordinates: A[30; 0] B[0; 0] C[13.86766666667; 7.98222024251]
Centroid: CG[14.62222222222; 2.66107341417]
Coordinates of the circumscribed circle: U[15; -10.02222965717]
Coordinates of the inscribed circle: I[14; 3.74216573868]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.6755423463° = 153°40'32″ = 0.45994505348 rad
∠ B' = β' = 150.0743565133° = 150°4'25″ = 0.52223148218 rad
∠ C' = γ' = 56.25110114041° = 56°15'4″ = 2.1659827297 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 = 16 ; ; b = 18 ; ; c = 30 ; ;

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

p = a+b+c = 16+18+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-16)(32-18)(32-30) } ; ; T = sqrt{ 14336 } = 119.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.73 }{ 16 } = 14.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.73 }{ 18 } = 13.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.73 }{ 30 } = 7.98 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 18**2+30**2-16**2 }{ 2 * 18 * 30 } ) = 26° 19'28" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16**2+30**2-18**2 }{ 2 * 16 * 30 } ) = 29° 55'35" ; ; gamma = 180° - alpha - beta = 180° - 26° 19'28" - 29° 55'35" = 123° 44'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.73 }{ 32 } = 3.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16 }{ 2 * sin 26° 19'28" } = 18.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 30**2 - 16**2 } }{ 2 } = 23.409 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 16**2 - 18**2 } }{ 2 } = 22.293 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 16**2 - 30**2 } }{ 2 } = 8.062 ; ;
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