5 17 17 triangle

Acute isosceles triangle.

Sides: a = 5   b = 17   c = 17

Area: T = 42.0387929302
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 16.91330386705° = 16°54'47″ = 0.29551882113 rad
Angle ∠ B = β = 81.54334806647° = 81°32'37″ = 1.42332022211 rad
Angle ∠ C = γ = 81.54334806647° = 81°32'37″ = 1.42332022211 rad

Height: ha = 16.81551717208
Height: hb = 4.94656387414
Height: hc = 4.94656387414

Median: ma = 16.81551717208
Median: mb = 9.20659763198
Median: mc = 9.20659763198

Inradius: r = 2.15657912463
Circumradius: R = 8.59334299334

Vertex coordinates: A[17; 0] B[0; 0] C[0.73552941176; 4.94656387414]
Centroid: CG[5.91217647059; 1.64985462471]
Coordinates of the circumscribed circle: U[8.5; 1.26437396961]
Coordinates of the inscribed circle: I[2.5; 2.15657912463]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0876961329° = 163°5'13″ = 0.29551882113 rad
∠ B' = β' = 98.45765193353° = 98°27'23″ = 1.42332022211 rad
∠ C' = γ' = 98.45765193353° = 98°27'23″ = 1.42332022211 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 = 5 ; ; b = 17 ; ; c = 17 ; ;

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

p = a+b+c = 5+17+17 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-5)(19.5-17)(19.5-17) } ; ; T = sqrt{ 1767.19 } = 42.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.04 }{ 5 } = 16.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.04 }{ 17 } = 4.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.04 }{ 17 } = 4.95 ; ;

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{ 5**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 16° 54'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-5**2-17**2 }{ 2 * 5 * 17 } ) = 81° 32'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-5**2-17**2 }{ 2 * 17 * 5 } ) = 81° 32'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.04 }{ 19.5 } = 2.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 16° 54'47" } = 8.59 ; ;




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