14 18 24 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 18   c = 24

Area: T = 125.221980674
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 35.43109446873° = 35°25'51″ = 0.61883866419 rad
Angle ∠ B = β = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ C = γ = 96.37993702084° = 96°22'46″ = 1.68221373411 rad

Height: ha = 17.889854382
Height: hb = 13.913331186
Height: hc = 10.4354983895

Median: ma = 20.02549843945
Median: mb = 17.46442491966
Median: mc = 10.77703296143

Inradius: r = 4.4722135955
Circumradius: R = 12.07547670785

Vertex coordinates: A[24; 0] B[0; 0] C[9.33333333333; 10.4354983895]
Centroid: CG[11.11111111111; 3.4788327965]
Coordinates of the circumscribed circle: U[12; -1.34216407865]
Coordinates of the inscribed circle: I[10; 4.4722135955]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.5699055313° = 144°34'9″ = 0.61883866419 rad
∠ B' = β' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ C' = γ' = 83.62106297916° = 83°37'14″ = 1.68221373411 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 = 24 ; ;

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

p = a+b+c = 14+18+24 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-14)(28-18)(28-24) } ; ; T = sqrt{ 15680 } = 125.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 125.22 }{ 14 } = 17.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 125.22 }{ 18 } = 13.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 125.22 }{ 24 } = 10.43 ; ;

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{ 14**2-18**2-24**2 }{ 2 * 18 * 24 } ) = 35° 25'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-14**2-24**2 }{ 2 * 14 * 24 } ) = 48° 11'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-14**2-18**2 }{ 2 * 18 * 14 } ) = 96° 22'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 125.22 }{ 28 } = 4.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 35° 25'51" } = 12.07 ; ;




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