1 25 25 triangle

Acute isosceles triangle.

Sides: a = 1   b = 25   c = 25

Area: T = 12.497749975
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 2.29219839968° = 2°17'31″ = 0.04400026671 rad
Angle ∠ B = β = 88.85440080016° = 88°51'14″ = 1.55107949932 rad
Angle ∠ C = γ = 88.85440080016° = 88°51'14″ = 1.55107949932 rad

Height: ha = 24.99549994999
Height: hb = 10.99979998
Height: hc = 10.99979998

Median: ma = 24.99549994999
Median: mb = 12.52199840255
Median: mc = 12.52199840255

Inradius: r = 0.49900980294
Circumradius: R = 12.50325007502

Vertex coordinates: A[25; 0] B[0; 0] C[0.02; 10.99979998]
Centroid: CG[8.34; 0.333326666]
Coordinates of the circumscribed circle: U[12.5; 0.2550050015]
Coordinates of the inscribed circle: I[0.5; 0.49900980294]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.7088016003° = 177°42'29″ = 0.04400026671 rad
∠ B' = β' = 91.14659919984° = 91°8'46″ = 1.55107949932 rad
∠ C' = γ' = 91.14659919984° = 91°8'46″ = 1.55107949932 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 = 1 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 1+25+25 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-1)(25.5-25)(25.5-25) } ; ; T = sqrt{ 156.19 } = 12.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.5 }{ 1 } = 24.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.5 }{ 25 } = 1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.5 }{ 25 } = 1 ; ;

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{ 1**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 2° 17'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-1**2-25**2 }{ 2 * 1 * 25 } ) = 88° 51'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-1**2-25**2 }{ 2 * 25 * 1 } ) = 88° 51'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.5 }{ 25.5 } = 0.49 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1 }{ 2 * sin 2° 17'31" } = 12.5 ; ;




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