400 900 984.9 triangle

Obtuse scalene triangle.

Sides: a = 400   b = 900   c = 984.9

Area: T = 1800009.999864
Perimeter: p = 2284.9
Semiperimeter: s = 1142.45

Angle ∠ A = α = 23.96221212995° = 23°57'44″ = 0.41882179124 rad
Angle ∠ B = β = 66.03656497356° = 66°2'8″ = 1.15325395116 rad
Angle ∠ C = γ = 90.0022228965° = 90°8″ = 1.57108352296 rad

Height: ha = 9009.999999319
Height: hb = 4009.999999697
Height: hc = 365.5199341789

Median: ma = 921.9622040976
Median: mb = 602.0911359347
Median: mc = 492.4365780077

Inradius: r = 157.5566129252
Circumradius: R = 492.4550000373

Vertex coordinates: A[984.9; 0] B[0; 0] C[162.4677260636; 365.5199341789]
Centroid: CG[382.4565753545; 121.8439780596]
Coordinates of the circumscribed circle: U[492.45; -0.01991576729]
Coordinates of the inscribed circle: I[242.45; 157.5566129252]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0387878701° = 156°2'16″ = 0.41882179124 rad
∠ B' = β' = 113.9644350264° = 113°57'52″ = 1.15325395116 rad
∠ C' = γ' = 89.9987771035° = 89°59'52″ = 1.57108352296 rad

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How did we calculate this triangle?

a = 400 ; ; b = 900 ; ; c = 984.9 ; ;

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

p = a+b+c = 400+900+984.9 = 2284.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2284.9 }{ 2 } = 1142.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1142.45 * (1142.45-400)(1142.45-900)(1142.45-984.9) } ; ; T = sqrt{ 32399999951 } = 180000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 180000 }{ 400 } = 900 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 180000 }{ 900 } = 400 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 180000 }{ 984.9 } = 365.52 ; ;

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{ 400**2-900**2-984.9**2 }{ 2 * 900 * 984.9 } ) = 23° 57'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 900**2-400**2-984.9**2 }{ 2 * 400 * 984.9 } ) = 66° 2'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 984.9**2-400**2-900**2 }{ 2 * 900 * 400 } ) = 90° 8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 180000 }{ 1142.45 } = 157.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 400 }{ 2 * sin 23° 57'44" } = 492.45 ; ;




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