Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 29.63   b = 57   c = 48.7

Area: T = 721.4990482978
Perimeter: p = 135.33
Semiperimeter: s = 67.665

Angle ∠ A = α = 31.32204833373° = 31°19'14″ = 0.54766455576 rad
Angle ∠ B = β = 89.98875539857° = 89°59'15″ = 1.57105791029 rad
Angle ∠ C = γ = 58.6921962677° = 58°41'31″ = 1.02443679932 rad

Height: ha = 48.7699998851
Height: hb = 25.31554555431
Height: hc = 29.63299993009

Median: ma = 50.99004987697
Median: mb = 28.50554985924
Median: mc = 38.34876981056

Inradius: r = 10.66326835584
Circumradius: R = 28.55000006724

Vertex coordinates: A[48.7; 0] B[0; 0] C[0.0066436345; 29.63299993009]
Centroid: CG[16.23554787817; 9.87766664336]
Coordinates of the circumscribed circle: U[24.35; 14.81097109468]
Coordinates of the inscribed circle: I[10.665; 10.66326835584]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.6879516663° = 148°40'46″ = 0.54766455576 rad
∠ B' = β' = 90.01224460143° = 90°45″ = 1.57105791029 rad
∠ C' = γ' = 121.3088037323° = 121°18'29″ = 1.02443679932 rad

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How did we calculate this triangle?

a = 29.63 ; ; b = 57 ; ; c = 48.7 ; ;

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

p = a+b+c = 29.63+57+48.7 = 135.33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 135.33 }{ 2 } = 67.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 67.67 * (67.67-29.63)(67.67-57)(67.67-48.7) } ; ; T = sqrt{ 520548.52 } = 721.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 721.49 }{ 29.63 } = 48.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 721.49 }{ 57 } = 25.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 721.49 }{ 48.7 } = 29.63 ; ;

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{ 57**2+48.7**2-29.63**2 }{ 2 * 57 * 48.7 } ) = 31° 19'14" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 29.63**2+48.7**2-57**2 }{ 2 * 29.63 * 48.7 } ) = 89° 59'15" ; ; gamma = 180° - alpha - beta = 180° - 31° 19'14" - 89° 59'15" = 58° 41'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 721.49 }{ 67.67 } = 10.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 29.63 }{ 2 * sin 31° 19'14" } = 28.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 57**2+2 * 48.7**2 - 29.63**2 } }{ 2 } = 50.9 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 48.7**2+2 * 29.63**2 - 57**2 } }{ 2 } = 28.505 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 57**2+2 * 29.63**2 - 48.7**2 } }{ 2 } = 38.348 ; ;
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