Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 2.5   b = 3.74   c = 2.78

Area: T = 3.47549992388
Perimeter: p = 9.02
Semiperimeter: s = 4.51

Angle ∠ A = α = 41.94774744169° = 41°56'51″ = 0.73221215415 rad
Angle ∠ B = β = 90.03879223892° = 90°2'17″ = 1.57114581973 rad
Angle ∠ C = γ = 48.01546031939° = 48°53″ = 0.83880129148 rad

Height: ha = 2.78799993911
Height: hb = 1.8588288363
Height: hc = 2.54999994524

Median: ma = 3.04988522431
Median: mb = 1.86987696487
Median: mc = 2.86112409895

Inradius: r = 0.77105098091
Circumradius: R = 1.87700004096

Vertex coordinates: A[2.78; 0] B[0; 0] C[-0.00216546763; 2.54999994524]
Centroid: CG[0.92661151079; 0.83333331508]
Coordinates of the circumscribed circle: U[1.39; 1.2510920274]
Coordinates of the inscribed circle: I[0.77; 0.77105098091]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0532525583° = 138°3'9″ = 0.73221215415 rad
∠ B' = β' = 89.96220776108° = 89°57'43″ = 1.57114581973 rad
∠ C' = γ' = 131.9855396806° = 131°59'7″ = 0.83880129148 rad

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How did we calculate this triangle?

a = 2.5 ; ; b = 3.74 ; ; c = 2.78 ; ;

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

p = a+b+c = 2.5+3.74+2.78 = 9.02 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 9.02 }{ 2 } = 4.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.51 * (4.51-2.5)(4.51-3.74)(4.51-2.78) } ; ; T = sqrt{ 12.08 } = 3.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.47 }{ 2.5 } = 2.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.47 }{ 3.74 } = 1.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.47 }{ 2.78 } = 2.5 ; ;

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{ 3.74**2+2.78**2-2.5**2 }{ 2 * 3.74 * 2.78 } ) = 41° 56'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.5**2+2.78**2-3.74**2 }{ 2 * 2.5 * 2.78 } ) = 90° 2'17" ; ; gamma = 180° - alpha - beta = 180° - 41° 56'51" - 90° 2'17" = 48° 53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.47 }{ 4.51 } = 0.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.5 }{ 2 * sin 41° 56'51" } = 1.87 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.74**2+2 * 2.78**2 - 2.5**2 } }{ 2 } = 3.049 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.78**2+2 * 2.5**2 - 3.74**2 } }{ 2 } = 1.869 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.74**2+2 * 2.5**2 - 2.78**2 } }{ 2 } = 2.861 ; ;
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