1000 1000 730 triangle

Acute isosceles triangle.

Sides: a = 1000   b = 1000   c = 730

Area: T = 339817.744435
Perimeter: p = 2730
Semiperimeter: s = 1365

Angle ∠ A = α = 68.59224172961° = 68°35'33″ = 1.19771635237 rad
Angle ∠ B = β = 68.59224172961° = 68°35'33″ = 1.19771635237 rad
Angle ∠ C = γ = 42.81551654077° = 42°48'55″ = 0.74772656062 rad

Height: ha = 679.63554887
Height: hb = 679.63554887
Height: hc = 931.0087518767

Median: ma = 718.6454557483
Median: mb = 718.6454557483
Median: mc = 931.0087518767

Inradius: r = 248.9510728461
Circumradius: R = 537.0532590792

Vertex coordinates: A[730; 0] B[0; 0] C[365; 931.0087518767]
Centroid: CG[365; 310.3365839589]
Coordinates of the circumscribed circle: U[365; 393.9554927975]
Coordinates of the inscribed circle: I[365; 248.9510728461]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111.4087582704° = 111°24'27″ = 1.19771635237 rad
∠ B' = β' = 111.4087582704° = 111°24'27″ = 1.19771635237 rad
∠ C' = γ' = 137.1854834592° = 137°11'5″ = 0.74772656062 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 = 1000 ; ; b = 1000 ; ; c = 730 ; ;

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

p = a+b+c = 1000+1000+730 = 2730 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2730 }{ 2 } = 1365 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1365 * (1365-1000)(1365-1000)(1365-730) } ; ; T = sqrt{ 115476099375 } = 339817.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 339817.74 }{ 1000 } = 679.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 339817.74 }{ 1000 } = 679.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 339817.74 }{ 730 } = 931.01 ; ;

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{ 1000**2-1000**2-730**2 }{ 2 * 1000 * 730 } ) = 68° 35'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1000**2-1000**2-730**2 }{ 2 * 1000 * 730 } ) = 68° 35'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 730**2-1000**2-1000**2 }{ 2 * 1000 * 1000 } ) = 42° 48'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 339817.74 }{ 1365 } = 248.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1000 }{ 2 * sin 68° 35'33" } = 537.05 ; ;




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