18 22 25 triangle

Acute scalene triangle.

Sides: a = 18   b = 22   c = 25

Area: T = 192.6421993086
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 44.46884446032° = 44°28'6″ = 0.77661207716 rad
Angle ∠ B = β = 58.89110774895° = 58°53'28″ = 1.02878432022 rad
Angle ∠ C = γ = 76.64404779074° = 76°38'26″ = 1.33876286798 rad

Height: ha = 21.40546658984
Height: hb = 17.51329084623
Height: hc = 15.41113594468

Median: ma = 21.7660055147
Median: mb = 18.8021595677
Median: mc = 15.74400762387

Inradius: r = 5.92774459411
Circumradius: R = 12.84876660792

Vertex coordinates: A[25; 0] B[0; 0] C[9.3; 15.41113594468]
Centroid: CG[11.43333333333; 5.13771198156]
Coordinates of the circumscribed circle: U[12.5; 2.96985895107]
Coordinates of the inscribed circle: I[10.5; 5.92774459411]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5321555397° = 135°31'54″ = 0.77661207716 rad
∠ B' = β' = 121.1098922511° = 121°6'32″ = 1.02878432022 rad
∠ C' = γ' = 103.3659522093° = 103°21'34″ = 1.33876286798 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 = 22 ; ; c = 25 ; ;

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

p = a+b+c = 18+22+25 = 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 * (32.5-18)(32.5-22)(32.5-25) } ; ; T = sqrt{ 37110.94 } = 192.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 192.64 }{ 18 } = 21.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 192.64 }{ 22 } = 17.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 192.64 }{ 25 } = 15.41 ; ;

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**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 44° 28'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 58° 53'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-18**2-22**2 }{ 2 * 22 * 18 } ) = 76° 38'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 192.64 }{ 32.5 } = 5.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 44° 28'6" } = 12.85 ; ;




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