Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 537.95   b = 390.27   c = 675

Area: T = 104915.1439711
Perimeter: p = 1603.22
Semiperimeter: s = 801.61

Angle ∠ A = α = 52.87995002995° = 52°47'58″ = 0.92215251236 rad
Angle ∠ B = β = 35.3300151928° = 35°18'1″ = 0.61661038776 rad
Angle ∠ C = γ = 91.99003477725° = 91°54'1″ = 1.60439636524 rad

Height: ha = 390.0555357229
Height: hb = 537.6544135397
Height: hc = 310.8659673217

Median: ma = 481.2699452412
Median: mb = 578.2999172596
Median: mc = 327.0233221958

Inradius: r = 130.8810527576
Circumradius: R = 337.686572219

Vertex coordinates: A[675; 0] B[0; 0] C[439.0440392296; 310.8659673217]
Centroid: CG[371.3476797432; 103.6219891072]
Coordinates of the circumscribed circle: U[337.5; -11.1988078908]
Coordinates of the inscribed circle: I[411.34; 130.8810527576]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.22004997° = 127°12'2″ = 0.92215251236 rad
∠ B' = β' = 144.7699848072° = 144°41'59″ = 0.61661038776 rad
∠ C' = γ' = 88.10996522275° = 88°5'59″ = 1.60439636524 rad

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How did we calculate this triangle?

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

p = a+b+c = 537.95+390.27+675 = 1603.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1603.22 }{ 2 } = 801.61 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 801.61 * (801.61-537.95)(801.61-390.27)(801.61-675) } ; ; T = sqrt{ 11007186540.5 } = 104915.14 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104915.14 }{ 537.95 } = 390.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104915.14 }{ 390.27 } = 537.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104915.14 }{ 675 } = 310.86 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 390.27**2+675**2-537.95**2 }{ 2 * 390.27 * 675 } ) = 52° 47'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 537.95**2+675**2-390.27**2 }{ 2 * 537.95 * 675 } ) = 35° 18'1" ; ; gamma = 180° - alpha - beta = 180° - 52° 47'58" - 35° 18'1" = 91° 54'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104915.14 }{ 801.61 } = 130.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 537.95 }{ 2 * sin 52° 47'58" } = 337.69 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 390.27**2+2 * 675**2 - 537.95**2 } }{ 2 } = 481.269 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 675**2+2 * 537.95**2 - 390.27**2 } }{ 2 } = 578.299 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 390.27**2+2 * 537.95**2 - 675**2 } }{ 2 } = 327.023 ; ;
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