14 18 23 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 23

Area: T = 125.9879909112
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 37.48882410762° = 37°29'18″ = 0.65442932376 rad
Angle ∠ B = β = 51.48985656201° = 51°29'19″ = 0.89986449972 rad
Angle ∠ C = γ = 91.02331933037° = 91°1'23″ = 1.58986544188 rad

Height: ha = 17.99771298732
Height: hb = 13.99877676792
Height: hc = 10.95547747054

Median: ma = 19.42993592277
Median: mb = 16.77879617356
Median: mc = 11.30326545555

Inradius: r = 4.58110876041
Circumradius: R = 11.50218339845

Vertex coordinates: A[23; 0] B[0; 0] C[8.71773913043; 10.95547747054]
Centroid: CG[10.57224637681; 3.65215915685]
Coordinates of the circumscribed circle: U[11.5; -0.20553898926]
Coordinates of the inscribed circle: I[9.5; 4.58110876041]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.5121758924° = 142°30'42″ = 0.65442932376 rad
∠ B' = β' = 128.511143438° = 128°30'41″ = 0.89986449972 rad
∠ C' = γ' = 88.97768066963° = 88°58'37″ = 1.58986544188 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 = 23 ; ;

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

p = a+b+c = 14+18+23 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-14)(27.5-18)(27.5-23) } ; ; T = sqrt{ 15870.94 } = 125.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 125.98 }{ 14 } = 18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 125.98 }{ 18 } = 14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 125.98 }{ 23 } = 10.95 ; ;

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**2-23**2 }{ 2 * 18 * 23 } ) = 37° 29'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-23**2 }{ 2 * 14 * 23 } ) = 51° 29'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 91° 1'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 125.98 }{ 27.5 } = 4.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 37° 29'18" } = 11.5 ; ;




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