10 25 25 triangle

Acute isosceles triangle.

Sides: a = 10   b = 25   c = 25

Area: T = 122.4744487139
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 78.46330409672° = 78°27'47″ = 1.3699438406 rad
Angle ∠ C = γ = 78.46330409672° = 78°27'47″ = 1.3699438406 rad

Height: ha = 24.49548974278
Height: hb = 9.79879589711
Height: hc = 9.79879589711

Median: ma = 24.49548974278
Median: mb = 14.36114066163
Median: mc = 14.36114066163

Inradius: r = 4.08224829046
Circumradius: R = 12.7587759077

Vertex coordinates: A[25; 0] B[0; 0] C[2; 9.79879589711]
Centroid: CG[9; 3.26659863237]
Coordinates of the circumscribed circle: U[12.5; 2.55215518154]
Coordinates of the inscribed circle: I[5; 4.08224829046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 101.5376959033° = 101°32'13″ = 1.3699438406 rad
∠ C' = γ' = 101.5376959033° = 101°32'13″ = 1.3699438406 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 = 10 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 10+25+25 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-10)(30-25)(30-25) } ; ; T = sqrt{ 15000 } = 122.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 122.47 }{ 10 } = 24.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 122.47 }{ 25 } = 9.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 122.47 }{ 25 } = 9.8 ; ;

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{ 10**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 23° 4'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-10**2-25**2 }{ 2 * 10 * 25 } ) = 78° 27'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-10**2-25**2 }{ 2 * 25 * 10 } ) = 78° 27'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 122.47 }{ 30 } = 4.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 23° 4'26" } = 12.76 ; ;




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