Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 33   b = 45   c = 18.26

Area: T = 260.9265890863
Perimeter: p = 96.26
Semiperimeter: s = 48.13

Angle ∠ A = α = 39.42765090517° = 39°25'35″ = 0.68881223955 rad
Angle ∠ B = β = 1209.999582785° = 119°59'58″ = 2.09443878206 rad
Angle ∠ C = γ = 20.57439081633° = 20°34'26″ = 0.35990824375 rad

Height: ha = 15.81436903553
Height: hb = 11.59767062606
Height: hc = 28.57989584734

Median: ma = 30.11658396861
Median: mb = 14.31765568486
Median: mc = 38.38880593414

Inradius: r = 5.42112734441
Circumradius: R = 25.9810652888

Vertex coordinates: A[18.26; 0] B[0; 0] C[-16.54997918949; 28.57989584734]
Centroid: CG[0.5876736035; 9.52663194911]
Coordinates of the circumscribed circle: U[9.13; 24.32435980991]
Coordinates of the inscribed circle: I[3.13; 5.42112734441]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.5733490948° = 140°34'25″ = 0.68881223955 rad
∠ B' = β' = 600.0004172151° = 60°2″ = 2.09443878206 rad
∠ C' = γ' = 159.4266091837° = 159°25'34″ = 0.35990824375 rad

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How did we calculate this triangle?

a = 33 ; ; b = 45 ; ; c = 18.26 ; ;

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

p = a+b+c = 33+45+18.26 = 96.26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 96.26 }{ 2 } = 48.13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 48.13 * (48.13-33)(48.13-45)(48.13-18.26) } ; ; T = sqrt{ 68082.32 } = 260.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 260.93 }{ 33 } = 15.81 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 260.93 }{ 45 } = 11.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 260.93 }{ 18.26 } = 28.58 ; ;

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{ 45**2+18.26**2-33**2 }{ 2 * 45 * 18.26 } ) = 39° 25'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 33**2+18.26**2-45**2 }{ 2 * 33 * 18.26 } ) = 119° 59'58" ; ; gamma = 180° - alpha - beta = 180° - 39° 25'35" - 119° 59'58" = 20° 34'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 260.93 }{ 48.13 } = 5.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 33 }{ 2 * sin 39° 25'35" } = 25.98 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 18.26**2 - 33**2 } }{ 2 } = 30.116 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18.26**2+2 * 33**2 - 45**2 } }{ 2 } = 14.317 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 45**2+2 * 33**2 - 18.26**2 } }{ 2 } = 38.388 ; ;
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