274 447 464 triangle

Acute scalene triangle.

Sides: a = 274   b = 447   c = 464

Area: T = 59399.38660527
Perimeter: p = 1185
Semiperimeter: s = 592.5

Angle ∠ A = α = 34.94441832341° = 34°56'39″ = 0.61098910519 rad
Angle ∠ B = β = 69.13550871679° = 69°8'6″ = 1.20766348997 rad
Angle ∠ C = γ = 75.9210729598° = 75°55'15″ = 1.3255066702 rad

Height: ha = 433.5722160969
Height: hb = 265.7699065113
Height: hc = 256.0321836434

Median: ma = 434.4922232382
Median: mb = 308.6599659754
Median: mc = 289.169863592

Inradius: r = 100.2522128359
Circumradius: R = 239.1855098435

Vertex coordinates: A[464; 0] B[0; 0] C[97.58994396552; 256.0321836434]
Centroid: CG[187.1966479885; 85.3443945478]
Coordinates of the circumscribed circle: U[232; 58.18551468454]
Coordinates of the inscribed circle: I[145.5; 100.2522128359]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.0565816766° = 145°3'21″ = 0.61098910519 rad
∠ B' = β' = 110.8654912832° = 110°51'54″ = 1.20766348997 rad
∠ C' = γ' = 104.0799270402° = 104°4'45″ = 1.3255066702 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 = 274 ; ; b = 447 ; ; c = 464 ; ;

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

p = a+b+c = 274+447+464 = 1185 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1185 }{ 2 } = 592.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 592.5 * (592.5-274)(592.5-447)(592.5-464) } ; ; T = sqrt{ 3528287063.44 } = 59399.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59399.39 }{ 274 } = 433.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59399.39 }{ 447 } = 265.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59399.39 }{ 464 } = 256.03 ; ;

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{ 274**2-447**2-464**2 }{ 2 * 447 * 464 } ) = 34° 56'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 447**2-274**2-464**2 }{ 2 * 274 * 464 } ) = 69° 8'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 464**2-274**2-447**2 }{ 2 * 447 * 274 } ) = 75° 55'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59399.39 }{ 592.5 } = 100.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 274 }{ 2 * sin 34° 56'39" } = 239.19 ; ;




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