Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 600   b = 108   c = 517.84

Area: T = 19497.95333322
Perimeter: p = 1225.84
Semiperimeter: s = 612.92

Angle ∠ A = α = 135.7921783758° = 135°47'30″ = 2.37700137237 rad
Angle ∠ B = β = 7.2110105909° = 7°12'36″ = 0.12658400875 rad
Angle ∠ C = γ = 36.99881103326° = 36°59'53″ = 0.64657388423 rad

Height: ha = 64.9933177774
Height: hb = 361.0733209856
Height: hc = 75.30549333084

Median: ma = 223.4087996276
Median: mb = 557.8219982432
Median: mc = 344.6632782441

Inradius: r = 31.81215795409
Circumradius: R = 430.2510696423

Vertex coordinates: A[517.84; 0] B[0; 0] C[595.256554766; 75.30549333084]
Centroid: CG[371.032184922; 25.10216444361]
Coordinates of the circumscribed circle: U[258.92; 343.6222023992]
Coordinates of the inscribed circle: I[504.92; 31.81215795409]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 44.20882162417° = 44°12'30″ = 2.37700137237 rad
∠ B' = β' = 172.7989894091° = 172°47'24″ = 0.12658400875 rad
∠ C' = γ' = 143.0021889667° = 143°7″ = 0.64657388423 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 = 600 ; ; b = 108 ; ; c = 517.84 ; ;

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

p = a+b+c = 600+108+517.84 = 1225.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1225.84 }{ 2 } = 612.92 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 612.92 * (612.92-600)(612.92-108)(612.92-517.84) } ; ; T = sqrt{ 380170184.14 } = 19497.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19497.95 }{ 600 } = 64.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19497.95 }{ 108 } = 361.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19497.95 }{ 517.84 } = 75.3 ; ;

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{ 600**2-108**2-517.84**2 }{ 2 * 108 * 517.84 } ) = 135° 47'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 108**2-600**2-517.84**2 }{ 2 * 600 * 517.84 } ) = 7° 12'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 517.84**2-600**2-108**2 }{ 2 * 108 * 600 } ) = 36° 59'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19497.95 }{ 612.92 } = 31.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 600 }{ 2 * sin 135° 47'30" } = 430.25 ; ;




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