Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, angle β and angle γ.

Right scalene triangle.

Sides: a = 654   b = 1039.216628681   c = 807.6232740374

Area: T = 264092.6366102
Perimeter: p = 2500.839902718
Semiperimeter: s = 1250.421951359

Angle ∠ A = α = 39° = 0.68106784083 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 51° = 0.89901179185 rad

Height: ha = 807.6232740374
Height: hb = 508.2533458793
Height: hc = 654

Median: ma = 871.3111362699
Median: mb = 519.6088143404
Median: mc = 768.6221898395

Inradius: r = 211.2033226782
Circumradius: R = 519.6088143404

Vertex coordinates: A[807.6232740374; 0] B[0; 0] C[-0; 654]
Centroid: CG[269.2087580125; 218]
Coordinates of the circumscribed circle: U[403.8111370187; 327]
Coordinates of the inscribed circle: I[211.2033226782; 211.2033226782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141° = 0.68106784083 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 129° = 0.89901179185 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 = 654 ; ; b = 1039.22 ; ; c = 807.62 ; ;

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

p = a+b+c = 654+1039.22+807.62 = 2500.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2500.84 }{ 2 } = 1250.42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1250.42 * (1250.42-654)(1250.42-1039.22)(1250.42-807.62) } ; ; T = sqrt{ 69744920443.4 } = 264092.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 264092.64 }{ 654 } = 807.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 264092.64 }{ 1039.22 } = 508.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 264092.64 }{ 807.62 } = 654 ; ;

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{ 654**2-1039.22**2-807.62**2 }{ 2 * 1039.22 * 807.62 } ) = 39° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1039.22**2-654**2-807.62**2 }{ 2 * 654 * 807.62 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 807.62**2-654**2-1039.22**2 }{ 2 * 1039.22 * 654 } ) = 51° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 264092.64 }{ 1250.42 } = 211.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 654 }{ 2 * sin 39° } = 519.61 ; ;




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