16 22 30 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 22   c = 30

Area: T = 171.3944282285
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 31.29904452139° = 31°17'26″ = 0.54661212934 rad
Angle ∠ B = β = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ C = γ = 103.1376558787° = 103°8'12″ = 1.880007253 rad

Height: ha = 21.42442852856
Height: hb = 15.58112983895
Height: hc = 11.42662854857

Median: ma = 25.06599281723
Median: mb = 21.37875583264
Median: mc = 12.04215945788

Inradius: r = 5.04110083025
Circumradius: R = 15.40330809243

Vertex coordinates: A[30; 0] B[0; 0] C[11.2; 11.42662854857]
Centroid: CG[13.73333333333; 3.80987618286]
Coordinates of the circumscribed circle: U[15; -3.50107002101]
Coordinates of the inscribed circle: I[12; 5.04110083025]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.7109554786° = 148°42'34″ = 0.54661212934 rad
∠ B' = β' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ C' = γ' = 76.86334412131° = 76°51'48″ = 1.880007253 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 = 22 ; ; c = 30 ; ;

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

p = a+b+c = 16+22+30 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-16)(34-22)(34-30) } ; ; T = sqrt{ 29376 } = 171.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 171.39 }{ 16 } = 21.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 171.39 }{ 22 } = 15.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 171.39 }{ 30 } = 11.43 ; ;

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**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 31° 17'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-16**2-30**2 }{ 2 * 16 * 30 } ) = 45° 34'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-16**2-22**2 }{ 2 * 22 * 16 } ) = 103° 8'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 171.39 }{ 34 } = 5.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 31° 17'26" } = 15.4 ; ;




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