3 17 17 triangle

Acute isosceles triangle.

Sides: a = 3   b = 17   c = 17

Area: T = 25.40105413328
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 10.12441859286° = 10°7'27″ = 0.17767003785 rad
Angle ∠ B = β = 84.93879070357° = 84°56'16″ = 1.48224461375 rad
Angle ∠ C = γ = 84.93879070357° = 84°56'16″ = 1.48224461375 rad

Height: ha = 16.93436942219
Height: hb = 2.98882989803
Height: hc = 2.98882989803

Median: ma = 16.93436942219
Median: mb = 8.7610707734
Median: mc = 8.7610707734

Inradius: r = 1.37330022342
Circumradius: R = 8.53332827029

Vertex coordinates: A[17; 0] B[0; 0] C[0.26547058824; 2.98882989803]
Centroid: CG[5.75549019608; 0.99660996601]
Coordinates of the circumscribed circle: U[8.5; 0.75329367091]
Coordinates of the inscribed circle: I[1.5; 1.37330022342]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.8765814071° = 169°52'33″ = 0.17767003785 rad
∠ B' = β' = 95.06220929643° = 95°3'44″ = 1.48224461375 rad
∠ C' = γ' = 95.06220929643° = 95°3'44″ = 1.48224461375 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 = 3 ; ; b = 17 ; ; c = 17 ; ;

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

p = a+b+c = 3+17+17 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-3)(18.5-17)(18.5-17) } ; ; T = sqrt{ 645.19 } = 25.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.4 }{ 3 } = 16.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.4 }{ 17 } = 2.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.4 }{ 17 } = 2.99 ; ;

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{ 3**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 10° 7'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-3**2-17**2 }{ 2 * 3 * 17 } ) = 84° 56'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-3**2-17**2 }{ 2 * 17 * 3 } ) = 84° 56'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.4 }{ 18.5 } = 1.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 10° 7'27" } = 8.53 ; ;




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