18 24 25 triangle

Acute scalene triangle.

Sides: a = 18   b = 24   c = 25

Area: T = 204.7676788079
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 43.04436991107° = 43°2'37″ = 0.75112542717 rad
Angle ∠ B = β = 65.51656646223° = 65°30'56″ = 1.14334640593 rad
Angle ∠ C = γ = 71.4410636267° = 71°26'26″ = 1.24768743226 rad

Height: ha = 22.75218653421
Height: hb = 17.06438990065
Height: hc = 16.38113430463

Median: ma = 22.79325426401
Median: mb = 18.18796589627
Median: mc = 17.1399136501

Inradius: r = 6.11224414352
Circumradius: R = 13.18657320483

Vertex coordinates: A[25; 0] B[0; 0] C[7.46; 16.38113430463]
Centroid: CG[10.82; 5.46604476821]
Coordinates of the circumscribed circle: U[12.5; 4.19768475848]
Coordinates of the inscribed circle: I[9.5; 6.11224414352]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.9566300889° = 136°57'23″ = 0.75112542717 rad
∠ B' = β' = 114.4844335378° = 114°29'4″ = 1.14334640593 rad
∠ C' = γ' = 108.5599363733° = 108°33'34″ = 1.24768743226 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 = 18 ; ; b = 24 ; ; c = 25 ; ;

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

p = a+b+c = 18+24+25 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-18)(33.5-24)(33.5-25) } ; ; T = sqrt{ 41929.44 } = 204.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 204.77 }{ 18 } = 22.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 204.77 }{ 24 } = 17.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 204.77 }{ 25 } = 16.38 ; ;

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{ 18**2-24**2-25**2 }{ 2 * 24 * 25 } ) = 43° 2'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 65° 30'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-18**2-24**2 }{ 2 * 24 * 18 } ) = 71° 26'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 204.77 }{ 33.5 } = 6.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 43° 2'37" } = 13.19 ; ;




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