18 25 25 triangle

Acute isosceles triangle.

Sides: a = 18   b = 25   c = 25

Area: T = 209.9144268214
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 42.22003920482° = 42°12'1″ = 0.73765357869 rad
Angle ∠ B = β = 68.98998039759° = 68°53'59″ = 1.20325284334 rad
Angle ∠ C = γ = 68.98998039759° = 68°53'59″ = 1.20325284334 rad

Height: ha = 23.32438075794
Height: hb = 16.79331414572
Height: hc = 16.79331414572

Median: ma = 23.32438075794
Median: mb = 17.84395627749
Median: mc = 17.84395627749

Inradius: r = 6.17439490651
Circumradius: R = 13.39883269643

Vertex coordinates: A[25; 0] B[0; 0] C[6.48; 16.79331414572]
Centroid: CG[10.49333333333; 5.59877138191]
Coordinates of the circumscribed circle: U[12.5; 4.82333977071]
Coordinates of the inscribed circle: I[9; 6.17439490651]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.8799607952° = 137°47'59″ = 0.73765357869 rad
∠ B' = β' = 111.1100196024° = 111°6'1″ = 1.20325284334 rad
∠ C' = γ' = 111.1100196024° = 111°6'1″ = 1.20325284334 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 = 25 ; ;

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

p = a+b+c = 18+25+25 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-18)(34-25)(34-25) } ; ; T = sqrt{ 44064 } = 209.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 209.91 }{ 18 } = 23.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 209.91 }{ 25 } = 16.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 209.91 }{ 25 } = 16.79 ; ;

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**2-25**2 }{ 2 * 25 * 25 } ) = 42° 12'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-18**2-25**2 }{ 2 * 18 * 25 } ) = 68° 53'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-18**2-25**2 }{ 2 * 25 * 18 } ) = 68° 53'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 209.91 }{ 34 } = 6.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 42° 12'1" } = 13.4 ; ;




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