16 17 18 triangle

Acute scalene triangle.

Sides: a = 16   b = 17   c = 18

Area: T = 124.2721627896
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 54.31546652873° = 54°18'53″ = 0.94879697414 rad
Angle ∠ B = β = 59.65548170304° = 59°39'17″ = 1.04111729719 rad
Angle ∠ C = γ = 66.03105176822° = 66°1'50″ = 1.15224499404 rad

Height: ha = 15.5343953487
Height: hb = 14.62201915172
Height: hc = 13.80879586551

Median: ma = 15.57224115024
Median: mb = 14.75663545634
Median: mc = 13.83883525031

Inradius: r = 4.87333971724
Circumradius: R = 9.849939218

Vertex coordinates: A[18; 0] B[0; 0] C[8.08333333333; 13.80879586551]
Centroid: CG[8.69444444444; 4.6032652885]
Coordinates of the circumscribed circle: U[9; 4.00113155731]
Coordinates of the inscribed circle: I[8.5; 4.87333971724]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.6855334713° = 125°41'7″ = 0.94879697414 rad
∠ B' = β' = 120.345518297° = 120°20'43″ = 1.04111729719 rad
∠ C' = γ' = 113.9699482318° = 113°58'10″ = 1.15224499404 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 = 17 ; ; c = 18 ; ;

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

p = a+b+c = 16+17+18 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-16)(25.5-17)(25.5-18) } ; ; T = sqrt{ 15443.44 } = 124.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 124.27 }{ 16 } = 15.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 124.27 }{ 17 } = 14.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 124.27 }{ 18 } = 13.81 ; ;

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**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 54° 18'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 59° 39'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-16**2-17**2 }{ 2 * 17 * 16 } ) = 66° 1'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 124.27 }{ 25.5 } = 4.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 54° 18'53" } = 9.85 ; ;




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