17 17 25 triangle

Obtuse isosceles triangle.

Sides: a = 17   b = 17   c = 25

Area: T = 144.0211482773
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 42.66879254941° = 42°40'5″ = 0.74546957849 rad
Angle ∠ B = β = 42.66879254941° = 42°40'5″ = 0.74546957849 rad
Angle ∠ C = γ = 94.66441490118° = 94°39'51″ = 1.65222010839 rad

Height: ha = 16.94437038556
Height: hb = 16.94437038556
Height: hc = 11.52217186218

Median: ma = 19.61550452459
Median: mb = 19.61550452459
Median: mc = 11.52217186218

Inradius: r = 4.88220841618
Circumradius: R = 12.54215317578

Vertex coordinates: A[25; 0] B[0; 0] C[12.5; 11.52217186218]
Centroid: CG[12.5; 3.84105728739]
Coordinates of the circumscribed circle: U[12.5; -1.0219813136]
Coordinates of the inscribed circle: I[12.5; 4.88220841618]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.3322074506° = 137°19'55″ = 0.74546957849 rad
∠ B' = β' = 137.3322074506° = 137°19'55″ = 0.74546957849 rad
∠ C' = γ' = 85.33658509882° = 85°20'9″ = 1.65222010839 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 = 17 ; ; b = 17 ; ; c = 25 ; ;

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

p = a+b+c = 17+17+25 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-17)(29.5-17)(29.5-25) } ; ; T = sqrt{ 20742.19 } = 144.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 144.02 }{ 17 } = 16.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 144.02 }{ 17 } = 16.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 144.02 }{ 25 } = 11.52 ; ;

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{ 17**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 42° 40'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-17**2-25**2 }{ 2 * 17 * 25 } ) = 42° 40'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 94° 39'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 144.02 }{ 29.5 } = 4.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 42° 40'5" } = 12.54 ; ;




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