16 20 27 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 20   c = 27

Area: T = 158.9565772151
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 36.06765882598° = 36°4' = 0.62994807151 rad
Angle ∠ B = β = 47.38438572905° = 47°23'2″ = 0.8277004322 rad
Angle ∠ C = γ = 96.55495544497° = 96°32'58″ = 1.68551076165 rad

Height: ha = 19.86994715188
Height: hb = 15.89655772151
Height: hc = 11.77545016408

Median: ma = 22.37218573212
Median: mb = 19.81216127562
Median: mc = 12.07326964676

Inradius: r = 5.04662149889
Circumradius: R = 13.58986855241

Vertex coordinates: A[27; 0] B[0; 0] C[10.83333333333; 11.77545016408]
Centroid: CG[12.61111111111; 3.92548338803]
Coordinates of the circumscribed circle: U[13.5; -1.55499594426]
Coordinates of the inscribed circle: I[11.5; 5.04662149889]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.933341174° = 143°56' = 0.62994807151 rad
∠ B' = β' = 132.6166142709° = 132°36'58″ = 0.8277004322 rad
∠ C' = γ' = 83.45504455503° = 83°27'2″ = 1.68551076165 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 = 20 ; ; c = 27 ; ;

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

p = a+b+c = 16+20+27 = 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 * (31.5-16)(31.5-20)(31.5-27) } ; ; T = sqrt{ 25266.94 } = 158.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 158.96 }{ 16 } = 19.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 158.96 }{ 20 } = 15.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 158.96 }{ 27 } = 11.77 ; ;

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{ 16**2-20**2-27**2 }{ 2 * 20 * 27 } ) = 36° 4' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-16**2-27**2 }{ 2 * 16 * 27 } ) = 47° 23'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-16**2-20**2 }{ 2 * 20 * 16 } ) = 96° 32'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 158.96 }{ 31.5 } = 5.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 36° 4' } = 13.59 ; ;




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