14 23 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 23   c = 28

Area: T = 160.3232916328
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 29.86109807915° = 29°51'40″ = 0.52111724327 rad
Angle ∠ B = β = 54.88325008958° = 54°52'57″ = 0.95878803424 rad
Angle ∠ C = γ = 95.25765183127° = 95°15'23″ = 1.66325398785 rad

Height: ha = 22.90332737612
Height: hb = 13.9411123159
Height: hc = 11.45216368806

Median: ma = 24.64875150877
Median: mb = 18.91442803194
Median: mc = 12.90334879006

Inradius: r = 4.93330128101
Circumradius: R = 14.05991254926

Vertex coordinates: A[28; 0] B[0; 0] C[8.05435714286; 11.45216368806]
Centroid: CG[12.01878571429; 3.81772122935]
Coordinates of the circumscribed circle: U[14; -1.28880254721]
Coordinates of the inscribed circle: I[9.5; 4.93330128101]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.1399019208° = 150°8'20″ = 0.52111724327 rad
∠ B' = β' = 125.1177499104° = 125°7'3″ = 0.95878803424 rad
∠ C' = γ' = 84.74334816873° = 84°44'37″ = 1.66325398785 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 = 23 ; ; c = 28 ; ;

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

p = a+b+c = 14+23+28 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-14)(32.5-23)(32.5-28) } ; ; T = sqrt{ 25703.44 } = 160.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 160.32 }{ 14 } = 22.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 160.32 }{ 23 } = 13.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 160.32 }{ 28 } = 11.45 ; ;

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**2-23**2-28**2 }{ 2 * 23 * 28 } ) = 29° 51'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 54° 52'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-23**2 }{ 2 * 23 * 14 } ) = 95° 15'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 160.32 }{ 32.5 } = 4.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 29° 51'40" } = 14.06 ; ;




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