200 200 350 triangle

Obtuse isosceles triangle.

Sides: a = 200   b = 200   c = 350

Area: T = 16944.30221397
Perimeter: p = 750
Semiperimeter: s = 375

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ C = γ = 122.0989951256° = 122°5'24″ = 2.1310871633 rad

Height: ha = 169.4433021397
Height: hb = 169.4433021397
Height: hc = 96.82545836552

Median: ma = 266.9276956301
Median: mb = 266.9276956301
Median: mc = 96.82545836552

Inradius: r = 45.18548057058
Circumradius: R = 206.5599111798

Vertex coordinates: A[350; 0] B[0; 0] C[175; 96.82545836552]
Centroid: CG[175; 32.27548612184]
Coordinates of the circumscribed circle: U[175; -109.7354528142]
Coordinates of the inscribed circle: I[175; 45.18548057058]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ C' = γ' = 57.91100487437° = 57°54'36″ = 2.1310871633 rad

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How did we calculate this triangle?

a = 200 ; ; b = 200 ; ; c = 350 ; ;

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

p = a+b+c = 200+200+350 = 750 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 750 }{ 2 } = 375 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 375 * (375-200)(375-200)(375-350) } ; ; T = sqrt{ 287109375 } = 16944.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16944.3 }{ 200 } = 169.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16944.3 }{ 200 } = 169.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16944.3 }{ 350 } = 96.82 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 200**2+350**2-200**2 }{ 2 * 200 * 350 } ) = 28° 57'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+350**2-200**2 }{ 2 * 200 * 350 } ) = 28° 57'18" ; ; gamma = 180° - alpha - beta = 180° - 28° 57'18" - 28° 57'18" = 122° 5'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16944.3 }{ 375 } = 45.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 28° 57'18" } = 206.56 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 350**2 - 200**2 } }{ 2 } = 266.927 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 350**2+2 * 200**2 - 200**2 } }{ 2 } = 266.927 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 200**2 - 350**2 } }{ 2 } = 96.825 ; ;
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