18 25 30 triangle

Acute scalene triangle.

Sides: a = 18   b = 25   c = 30

Area: T = 224.6666280291
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 36.80661884285° = 36°48'22″ = 0.64223891732 rad
Angle ∠ B = β = 56.315479162° = 56°18'53″ = 0.98328785313 rad
Angle ∠ C = γ = 86.87990199516° = 86°52'44″ = 1.51663249491 rad

Height: ha = 24.96329200324
Height: hb = 17.97333024233
Height: hc = 14.97877520194

Median: ma = 26.10655549644
Median: mb = 21.34883020402
Median: mc = 15.79655689989

Inradius: r = 6.15552405559
Circumradius: R = 15.02222810278

Vertex coordinates: A[30; 0] B[0; 0] C[9.98333333333; 14.97877520194]
Centroid: CG[13.32877777778; 4.99325840065]
Coordinates of the circumscribed circle: U[15; 0.81878797448]
Coordinates of the inscribed circle: I[11.5; 6.15552405559]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1943811572° = 143°11'38″ = 0.64223891732 rad
∠ B' = β' = 123.685520838° = 123°41'7″ = 0.98328785313 rad
∠ C' = γ' = 93.12109800484° = 93°7'16″ = 1.51663249491 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 = 25 ; ; c = 30 ; ;

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

p = a+b+c = 18+25+30 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-18)(36.5-25)(36.5-30) } ; ; T = sqrt{ 50474.94 } = 224.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 224.67 }{ 18 } = 24.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 224.67 }{ 25 } = 17.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 224.67 }{ 30 } = 14.98 ; ;

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**2-25**2-30**2 }{ 2 * 25 * 30 } ) = 36° 48'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 56° 18'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-18**2-25**2 }{ 2 * 25 * 18 } ) = 86° 52'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 224.67 }{ 36.5 } = 6.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 36° 48'22" } = 15.02 ; ;




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