3 16 18 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 16   c = 18

Area: T = 18.93224456952
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 7.55548535785° = 7°33'17″ = 0.13218570695 rad
Angle ∠ B = β = 44.52334956372° = 44°31'25″ = 0.77770815934 rad
Angle ∠ C = γ = 127.9221650784° = 127°55'18″ = 2.23326539908 rad

Height: ha = 12.62216304634
Height: hb = 2.36765557119
Height: hc = 2.10436050772

Median: ma = 16.96331954537
Median: mb = 10.12442283657
Median: mc = 7.17663500472

Inradius: r = 1.0233375443
Circumradius: R = 11.40989855837

Vertex coordinates: A[18; 0] B[0; 0] C[2.13988888889; 2.10436050772]
Centroid: CG[6.7132962963; 0.70112016924]
Coordinates of the circumscribed circle: U[9; -7.012177239]
Coordinates of the inscribed circle: I[2.5; 1.0233375443]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.4455146422° = 172°26'43″ = 0.13218570695 rad
∠ B' = β' = 135.4776504363° = 135°28'35″ = 0.77770815934 rad
∠ C' = γ' = 52.07883492157° = 52°4'42″ = 2.23326539908 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 = 3 ; ; b = 16 ; ; c = 18 ; ;

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

p = a+b+c = 3+16+18 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-3)(18.5-16)(18.5-18) } ; ; T = sqrt{ 358.44 } = 18.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.93 }{ 3 } = 12.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.93 }{ 16 } = 2.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.93 }{ 18 } = 2.1 ; ;

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{ 3**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 7° 33'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-3**2-18**2 }{ 2 * 3 * 18 } ) = 44° 31'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-3**2-16**2 }{ 2 * 16 * 3 } ) = 127° 55'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.93 }{ 18.5 } = 1.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 7° 33'17" } = 11.41 ; ;




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