18 20 25 triangle

Acute scalene triangle.

Sides: a = 18   b = 20   c = 25

Area: T = 178.2990318021
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 45.49327106983° = 45°29'34″ = 0.79439975873 rad
Angle ∠ B = β = 52.41104970351° = 52°24'38″ = 0.91547357359 rad
Angle ∠ C = γ = 82.09767922665° = 82°5'48″ = 1.43328593304 rad

Height: ha = 19.81100353357
Height: hb = 17.82990318021
Height: hc = 14.26332254417

Median: ma = 20.77325780778
Median: mb = 19.35220024804
Median: mc = 14.34439882878

Inradius: r = 5.66600100959
Circumradius: R = 12.62198664346

Vertex coordinates: A[25; 0] B[0; 0] C[10.98; 14.26332254417]
Centroid: CG[11.99333333333; 4.75444084806]
Coordinates of the circumscribed circle: U[12.5; 1.73552316348]
Coordinates of the inscribed circle: I[11.5; 5.66600100959]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.5077289302° = 134°30'26″ = 0.79439975873 rad
∠ B' = β' = 127.5989502965° = 127°35'22″ = 0.91547357359 rad
∠ C' = γ' = 97.90332077335° = 97°54'12″ = 1.43328593304 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 = 20 ; ; c = 25 ; ;

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

p = a+b+c = 18+20+25 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-18)(31.5-20)(31.5-25) } ; ; T = sqrt{ 31787.44 } = 178.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 178.29 }{ 18 } = 19.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 178.29 }{ 20 } = 17.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 178.29 }{ 25 } = 14.26 ; ;

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**2-20**2-25**2 }{ 2 * 20 * 25 } ) = 45° 29'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 52° 24'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-18**2-20**2 }{ 2 * 20 * 18 } ) = 82° 5'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 178.29 }{ 31.5 } = 5.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 45° 29'34" } = 12.62 ; ;




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