13 25 25 triangle

Acute isosceles triangle.

Sides: a = 13   b = 25   c = 25

Area: T = 156.911140016
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 30.14401242898° = 30°8'24″ = 0.52660444058 rad
Angle ∠ B = β = 74.93299378551° = 74°55'48″ = 1.30877741239 rad
Angle ∠ C = γ = 74.93299378551° = 74°55'48″ = 1.30877741239 rad

Height: ha = 24.14402154091
Height: hb = 12.55329120128
Height: hc = 12.55329120128

Median: ma = 24.14402154091
Median: mb = 15.51661206492
Median: mc = 15.51661206492

Inradius: r = 4.98113142908
Circumradius: R = 12.94552034584

Vertex coordinates: A[25; 0] B[0; 0] C[3.38; 12.55329120128]
Centroid: CG[9.46; 4.18443040043]
Coordinates of the circumscribed circle: U[12.5; 3.36657528992]
Coordinates of the inscribed circle: I[6.5; 4.98113142908]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.865987571° = 149°51'36″ = 0.52660444058 rad
∠ B' = β' = 105.0770062145° = 105°4'12″ = 1.30877741239 rad
∠ C' = γ' = 105.0770062145° = 105°4'12″ = 1.30877741239 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 = 13 ; ; b = 25 ; ; c = 25 ; ;

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

p = a+b+c = 13+25+25 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-13)(31.5-25)(31.5-25) } ; ; T = sqrt{ 24621.19 } = 156.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 156.91 }{ 13 } = 24.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 156.91 }{ 25 } = 12.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 156.91 }{ 25 } = 12.55 ; ;

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{ 13**2-25**2-25**2 }{ 2 * 25 * 25 } ) = 30° 8'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-13**2-25**2 }{ 2 * 13 * 25 } ) = 74° 55'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-13**2-25**2 }{ 2 * 25 * 13 } ) = 74° 55'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 156.91 }{ 31.5 } = 4.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 30° 8'24" } = 12.95 ; ;




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