25 25 27 triangle

Acute isosceles triangle.

Sides: a = 25   b = 25   c = 27

Area: T = 284.0621943069
Perimeter: p = 77
Semiperimeter: s = 38.5

Angle ∠ A = α = 57.31663611537° = 57°18'59″ = 11.0003592174 rad
Angle ∠ B = β = 57.31663611537° = 57°18'59″ = 11.0003592174 rad
Angle ∠ C = γ = 65.36772776925° = 65°22'2″ = 1.14108742188 rad

Height: ha = 22.72549554455
Height: hb = 22.72549554455
Height: hc = 21.04216254125

Median: ma = 22.82199474145
Median: mb = 22.82199474145
Median: mc = 21.04216254125

Inradius: r = 7.37882322875
Circumradius: R = 14.85215142663

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 21.04216254125]
Centroid: CG[13.5; 7.01438751375]
Coordinates of the circumscribed circle: U[13.5; 6.19901111462]
Coordinates of the inscribed circle: I[13.5; 7.37882322875]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.6843638846° = 122°41'1″ = 11.0003592174 rad
∠ B' = β' = 122.6843638846° = 122°41'1″ = 11.0003592174 rad
∠ C' = γ' = 114.6332722307° = 114°37'58″ = 1.14108742188 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 = 25 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 25+25+27 = 77 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 77 }{ 2 } = 38.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38.5 * (38.5-25)(38.5-25)(38.5-27) } ; ; T = sqrt{ 80691.19 } = 284.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 284.06 }{ 25 } = 22.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 284.06 }{ 25 } = 22.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 284.06 }{ 27 } = 21.04 ; ;

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{ 25**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 57° 18'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 57° 18'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 65° 22'2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 284.06 }{ 38.5 } = 7.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 25 }{ 2 * sin 57° 18'59" } = 14.85 ; ;




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