200 200 153.07 triangle

Acute isosceles triangle.

Sides: a = 200   b = 200   c = 153.07

Area: T = 14141.87774677
Perimeter: p = 553.07
Semiperimeter: s = 276.535

Angle ∠ A = α = 67.50105229448° = 67°30'2″ = 1.17881063722 rad
Angle ∠ B = β = 67.50105229448° = 67°30'2″ = 1.17881063722 rad
Angle ∠ C = γ = 44.99989541104° = 44°59'56″ = 0.78553799092 rad

Height: ha = 141.4198774678
Height: hb = 141.4198774678
Height: hc = 184.7776605053

Median: ma = 147.3610824
Median: mb = 147.3610824
Median: mc = 184.7776605053

Inradius: r = 51.14395572631
Circumradius: R = 108.2398810829

Vertex coordinates: A[153.07; 0] B[0; 0] C[76.535; 184.7776605053]
Centroid: CG[76.535; 61.59222016844]
Coordinates of the circumscribed circle: U[76.535; 76.53877942241]
Coordinates of the inscribed circle: I[76.535; 51.14395572631]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.4999477055° = 112°29'58″ = 1.17881063722 rad
∠ B' = β' = 112.4999477055° = 112°29'58″ = 1.17881063722 rad
∠ C' = γ' = 135.001104589° = 135°4″ = 0.78553799092 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 = 200 ; ; b = 200 ; ; c = 153.07 ; ;

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

p = a+b+c = 200+200+153.07 = 553.07 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 553.07 }{ 2 } = 276.54 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 276.54 * (276.54-200)(276.54-200)(276.54-153.07) } ; ; T = sqrt{ 199992698.31 } = 14141.88 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14141.88 }{ 200 } = 141.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14141.88 }{ 200 } = 141.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14141.88 }{ 153.07 } = 184.78 ; ;

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+153.07**2-200**2 }{ 2 * 200 * 153.07 } ) = 67° 30'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+153.07**2-200**2 }{ 2 * 200 * 153.07 } ) = 67° 30'2" ; ; gamma = 180° - alpha - beta = 180° - 67° 30'2" - 67° 30'2" = 44° 59'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14141.88 }{ 276.54 } = 51.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 67° 30'2" } = 108.24 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 153.07**2 - 200**2 } }{ 2 } = 147.361 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 153.07**2+2 * 200**2 - 200**2 } }{ 2 } = 147.361 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 200**2 - 153.07**2 } }{ 2 } = 184.777 ; ;
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