14 14 25 triangle

Obtuse isosceles triangle.

Sides: a = 14   b = 14   c = 25

Area: T = 78.81095013307
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 26.76655005768° = 26°45'56″ = 0.4677146111 rad
Angle ∠ B = β = 26.76655005768° = 26°45'56″ = 0.4677146111 rad
Angle ∠ C = γ = 126.4698998846° = 126°28'8″ = 2.20773004316 rad

Height: ha = 11.25985001901
Height: hb = 11.25985001901
Height: hc = 6.30547601065

Median: ma = 19.01331533418
Median: mb = 19.01331533418
Median: mc = 6.30547601065

Inradius: r = 2.97439434464
Circumradius: R = 15.54438110801

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 6.30547601065]
Centroid: CG[12.5; 2.10215867022]
Coordinates of the circumscribed circle: U[12.5; -9.23990509736]
Coordinates of the inscribed circle: I[12.5; 2.97439434464]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.2344499423° = 153°14'4″ = 0.4677146111 rad
∠ B' = β' = 153.2344499423° = 153°14'4″ = 0.4677146111 rad
∠ C' = γ' = 53.53110011535° = 53°31'52″ = 2.20773004316 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 = 14 ; ; b = 14 ; ; c = 25 ; ;

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

p = a+b+c = 14+14+25 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-14)(26.5-14)(26.5-25) } ; ; T = sqrt{ 6210.94 } = 78.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 78.81 }{ 14 } = 11.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 78.81 }{ 14 } = 11.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 78.81 }{ 25 } = 6.3 ; ;

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{ 14**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 26° 45'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-14**2-25**2 }{ 2 * 14 * 25 } ) = 26° 45'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 126° 28'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 78.81 }{ 26.5 } = 2.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 26° 45'56" } = 15.54 ; ;




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