17 17 30 triangle

Obtuse isosceles triangle.

Sides: a = 17   b = 17   c = 30

Area: T = 120
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ B = β = 28.07224869359° = 28°4'21″ = 0.49899573263 rad
Angle ∠ C = γ = 123.8555026128° = 123°51'18″ = 2.16216780011 rad

Height: ha = 14.11876470588
Height: hb = 14.11876470588
Height: hc = 8

Median: ma = 22.85327897641
Median: mb = 22.85327897641
Median: mc = 8

Inradius: r = 3.75
Circumradius: R = 18.06325

Vertex coordinates: A[30; 0] B[0; 0] C[15; 8]
Centroid: CG[15; 2.66766666667]
Coordinates of the circumscribed circle: U[15; -10.06325]
Coordinates of the inscribed circle: I[15; 3.75]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.9287513064° = 151°55'39″ = 0.49899573263 rad
∠ B' = β' = 151.9287513064° = 151°55'39″ = 0.49899573263 rad
∠ C' = γ' = 56.14549738717° = 56°8'42″ = 2.16216780011 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 = 17 ; ; b = 17 ; ; c = 30 ; ;

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

p = a+b+c = 17+17+30 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-17)(32-17)(32-30) } ; ; T = sqrt{ 14400 } = 120 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 120 }{ 17 } = 14.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 120 }{ 17 } = 14.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 120 }{ 30 } = 8 ; ;

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{ 17**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 28° 4'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 28° 4'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 123° 51'18" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 120 }{ 32 } = 3.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 28° 4'21" } = 18.06 ; ;




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