4 17 17 triangle

Acute isosceles triangle.

Sides: a = 4   b = 17   c = 17

Area: T = 33.76438860323
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 13.51326540612° = 13°30'46″ = 0.23658403041 rad
Angle ∠ B = β = 83.24436729694° = 83°14'37″ = 1.45328761748 rad
Angle ∠ C = γ = 83.24436729694° = 83°14'37″ = 1.45328761748 rad

Height: ha = 16.88219430161
Height: hb = 3.97222218861
Height: hc = 3.97222218861

Median: ma = 16.88219430161
Median: mb = 8.95882364336
Median: mc = 8.95882364336

Inradius: r = 1.77770466333
Circumradius: R = 8.55994412836

Vertex coordinates: A[17; 0] B[0; 0] C[0.47105882353; 3.97222218861]
Centroid: CG[5.82435294118; 1.3244073962]
Coordinates of the circumscribed circle: U[8.5; 1.00769930922]
Coordinates of the inscribed circle: I[2; 1.77770466333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.4877345939° = 166°29'14″ = 0.23658403041 rad
∠ B' = β' = 96.75663270306° = 96°45'23″ = 1.45328761748 rad
∠ C' = γ' = 96.75663270306° = 96°45'23″ = 1.45328761748 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 = 4 ; ; b = 17 ; ; c = 17 ; ;

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

p = a+b+c = 4+17+17 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-4)(19-17)(19-17) } ; ; T = sqrt{ 1140 } = 33.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.76 }{ 4 } = 16.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.76 }{ 17 } = 3.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.76 }{ 17 } = 3.97 ; ;

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{ 4**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 13° 30'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-4**2-17**2 }{ 2 * 4 * 17 } ) = 83° 14'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-4**2-17**2 }{ 2 * 17 * 4 } ) = 83° 14'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.76 }{ 19 } = 1.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 13° 30'46" } = 8.56 ; ;




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