14 18 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 28

Area: T = 107.331126292
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 25.20987652968° = 25°12'32″ = 0.44399759548 rad
Angle ∠ B = β = 33.2033099198° = 33°12'11″ = 0.58795034029 rad
Angle ∠ C = γ = 121.5888135505° = 121°35'17″ = 2.12221132959 rad

Height: ha = 15.333303756
Height: hb = 11.926569588
Height: hc = 7.667651878

Median: ma = 22.47222050542
Median: mb = 20.22437484162
Median: mc = 8

Inradius: r = 3.5787708764
Circumradius: R = 16.43550996346

Vertex coordinates: A[28; 0] B[0; 0] C[11.71442857143; 7.667651878]
Centroid: CG[13.23880952381; 2.556550626]
Coordinates of the circumscribed circle: U[14; -8.60988617134]
Coordinates of the inscribed circle: I[12; 3.5787708764]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.7911234703° = 154°47'28″ = 0.44399759548 rad
∠ B' = β' = 146.7976900802° = 146°47'49″ = 0.58795034029 rad
∠ C' = γ' = 58.41218644948° = 58°24'43″ = 2.12221132959 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 = 14 ; ; b = 18 ; ; c = 28 ; ;

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

p = a+b+c = 14+18+28 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-14)(30-18)(30-28) } ; ; T = sqrt{ 11520 } = 107.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.33 }{ 14 } = 15.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.33 }{ 18 } = 11.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.33 }{ 28 } = 7.67 ; ;

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{ 14**2-18**2-28**2 }{ 2 * 18 * 28 } ) = 25° 12'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 33° 12'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 121° 35'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.33 }{ 30 } = 3.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 25° 12'32" } = 16.44 ; ;




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