8 17 17 triangle

Acute isosceles triangle.

Sides: a = 8   b = 17   c = 17

Area: T = 66.09108465674
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 27.21879212616° = 27°13'5″ = 0.47550423416 rad
Angle ∠ B = β = 76.39110393692° = 76°23'28″ = 1.3333275156 rad
Angle ∠ C = γ = 76.39110393692° = 76°23'28″ = 1.3333275156 rad

Height: ha = 16.52327116419
Height: hb = 7.77553937138
Height: hc = 7.77553937138

Median: ma = 16.52327116419
Median: mb = 10.21102889283
Median: mc = 10.21102889283

Inradius: r = 3.14771831699
Circumradius: R = 8.74655378471

Vertex coordinates: A[17; 0] B[0; 0] C[1.88223529412; 7.77553937138]
Centroid: CG[6.29441176471; 2.59217979046]
Coordinates of the circumscribed circle: U[8.5; 2.05877736111]
Coordinates of the inscribed circle: I[4; 3.14771831699]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.7822078738° = 152°46'55″ = 0.47550423416 rad
∠ B' = β' = 103.6098960631° = 103°36'32″ = 1.3333275156 rad
∠ C' = γ' = 103.6098960631° = 103°36'32″ = 1.3333275156 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 = 8 ; ; b = 17 ; ; c = 17 ; ;

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

p = a+b+c = 8+17+17 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-8)(21-17)(21-17) } ; ; T = sqrt{ 4368 } = 66.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.09 }{ 8 } = 16.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.09 }{ 17 } = 7.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.09 }{ 17 } = 7.78 ; ;

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{ 8**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 27° 13'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 76° 23'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-8**2-17**2 }{ 2 * 17 * 8 } ) = 76° 23'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.09 }{ 21 } = 3.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 27° 13'5" } = 8.75 ; ;




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