12 17 17 triangle

Acute isosceles triangle.

Sides: a = 12   b = 17   c = 17

Area: T = 95.43658423235
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 41.3354632987° = 41°20'5″ = 0.72114254407 rad
Angle ∠ B = β = 69.33326835065° = 69°19'58″ = 1.21100836064 rad
Angle ∠ C = γ = 69.33326835065° = 69°19'58″ = 1.21100836064 rad

Height: ha = 15.90659737206
Height: hb = 11.22877461557
Height: hc = 11.22877461557

Median: ma = 15.90659737206
Median: mb = 12.01104121495
Median: mc = 12.01104121495

Inradius: r = 4.14993844488
Circumradius: R = 9.08546371645

Vertex coordinates: A[17; 0] B[0; 0] C[4.23552941176; 11.22877461557]
Centroid: CG[7.07884313725; 3.74325820519]
Coordinates of the circumscribed circle: U[8.5; 3.20663425287]
Coordinates of the inscribed circle: I[6; 4.14993844488]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.6655367013° = 138°39'55″ = 0.72114254407 rad
∠ B' = β' = 110.6677316494° = 110°40'2″ = 1.21100836064 rad
∠ C' = γ' = 110.6677316494° = 110°40'2″ = 1.21100836064 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 = 12 ; ; b = 17 ; ; c = 17 ; ;

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

p = a+b+c = 12+17+17 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-12)(23-17)(23-17) } ; ; T = sqrt{ 9108 } = 95.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 95.44 }{ 12 } = 15.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 95.44 }{ 17 } = 11.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 95.44 }{ 17 } = 11.23 ; ;

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{ 12**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 41° 20'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-12**2-17**2 }{ 2 * 12 * 17 } ) = 69° 19'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-12**2-17**2 }{ 2 * 17 * 12 } ) = 69° 19'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 95.44 }{ 23 } = 4.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 41° 20'5" } = 9.08 ; ;




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