18 23 25 triangle

Acute scalene triangle.

Sides: a = 18   b = 23   c = 25

Area: T = 198.9977487421
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 43.80217464419° = 43°48'6″ = 0.76444846935 rad
Angle ∠ B = β = 62.18218607153° = 62°10'55″ = 1.08552782045 rad
Angle ∠ C = γ = 74.01663928427° = 74°59″ = 1.29218297556 rad

Height: ha = 22.11108319357
Height: hb = 17.3044129341
Height: hc = 15.92197989937

Median: ma = 22.27110574513
Median: mb = 18.5
Median: mc = 16.43992822228

Inradius: r = 6.03302268916
Circumradius: R = 13.00326767349

Vertex coordinates: A[25; 0] B[0; 0] C[8.4; 15.92197989937]
Centroid: CG[11.13333333333; 5.30765996646]
Coordinates of the circumscribed circle: U[12.5; 3.58804472169]
Coordinates of the inscribed circle: I[10; 6.03302268916]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.1988253558° = 136°11'54″ = 0.76444846935 rad
∠ B' = β' = 117.8188139285° = 117°49'5″ = 1.08552782045 rad
∠ C' = γ' = 105.9843607157° = 105°59'1″ = 1.29218297556 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 = 23 ; ; c = 25 ; ;

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

p = a+b+c = 18+23+25 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-18)(33-23)(33-25) } ; ; T = sqrt{ 39600 } = 199 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 199 }{ 18 } = 22.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 199 }{ 23 } = 17.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 199 }{ 25 } = 15.92 ; ;

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**2-23**2-25**2 }{ 2 * 23 * 25 } ) = 43° 48'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 62° 10'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-18**2-23**2 }{ 2 * 23 * 18 } ) = 74° 59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 199 }{ 33 } = 6.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 43° 48'6" } = 13 ; ;




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