2 25 25 triangle

Acute isosceles triangle.

Sides: a = 2   b = 25   c = 25

Area: T = 24.98799919936
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 4.58548855519° = 4°35'6″ = 0.08800213487 rad
Angle ∠ B = β = 87.7087557224° = 87°42'27″ = 1.53107856524 rad
Angle ∠ C = γ = 87.7087557224° = 87°42'27″ = 1.53107856524 rad

Height: ha = 24.98799919936
Height: hb = 1.99883993595
Height: hc = 1.99883993595

Median: ma = 24.98799919936
Median: mb = 12.58797456254
Median: mc = 12.58797456254

Inradius: r = 0.96107689228
Circumradius: R = 12.5110012016

Vertex coordinates: A[25; 0] B[0; 0] C[0.08; 1.99883993595]
Centroid: CG[8.36; 0.66661331198]
Coordinates of the circumscribed circle: U[12.5; 0.55004004806]
Coordinates of the inscribed circle: I[1; 0.96107689228]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.4155114448° = 175°24'54″ = 0.08800213487 rad
∠ B' = β' = 92.2922442776° = 92°17'33″ = 1.53107856524 rad
∠ C' = γ' = 92.2922442776° = 92°17'33″ = 1.53107856524 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 = 2 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 2+25+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-2)(26-25)(26-25) } ; ; T = sqrt{ 624 } = 24.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.98 }{ 2 } = 24.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.98 }{ 25 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.98 }{ 25 } = 2 ; ;

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{ 2**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 4° 35'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-2**2-25**2 }{ 2 * 2 * 25 } ) = 87° 42'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-2**2-25**2 }{ 2 * 25 * 2 } ) = 87° 42'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.98 }{ 26 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 35'6" } = 12.51 ; ;




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