Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 60   b = 42   c = 29.33

Area: T = 565.5655316147
Perimeter: p = 131.33
Semiperimeter: s = 65.665

Angle ∠ A = α = 113.3311344124° = 113°19'53″ = 1.97880051007 rad
Angle ∠ B = β = 39.99880023163° = 39°59'53″ = 0.69880968346 rad
Angle ∠ C = γ = 26.67106535601° = 26°40'14″ = 0.46554907183 rad

Height: ha = 18.85221772049
Height: hb = 26.93216817213
Height: hc = 38.56656540161

Median: ma = 20.30108485044
Median: mb = 42.29880430989
Median: mc = 49.66882773508

Inradius: r = 8.61328883903
Circumradius: R = 32.67215579482

Vertex coordinates: A[29.33; 0] B[0; 0] C[45.96440112513; 38.56656540161]
Centroid: CG[25.09880037504; 12.85552180054]
Coordinates of the circumscribed circle: U[14.665; 29.1955350208]
Coordinates of the inscribed circle: I[23.665; 8.61328883903]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 66.66986558764° = 66°40'7″ = 1.97880051007 rad
∠ B' = β' = 140.0021997684° = 140°7″ = 0.69880968346 rad
∠ C' = γ' = 153.329934644° = 153°19'46″ = 0.46554907183 rad

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How did we calculate this triangle?

a = 60 ; ; b = 42 ; ; c = 29.33 ; ;

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

p = a+b+c = 60+42+29.33 = 131.33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 131.33 }{ 2 } = 65.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 65.67 * (65.67-60)(65.67-42)(65.67-29.33) } ; ; T = sqrt{ 319864.13 } = 565.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 565.57 }{ 60 } = 18.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 565.57 }{ 42 } = 26.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 565.57 }{ 29.33 } = 38.57 ; ;

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{ 42**2+29.33**2-60**2 }{ 2 * 42 * 29.33 } ) = 113° 19'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 60**2+29.33**2-42**2 }{ 2 * 60 * 29.33 } ) = 39° 59'53" ; ; gamma = 180° - alpha - beta = 180° - 113° 19'53" - 39° 59'53" = 26° 40'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 565.57 }{ 65.67 } = 8.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 60 }{ 2 * sin 113° 19'53" } = 32.67 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 29.33**2 - 60**2 } }{ 2 } = 20.301 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.33**2+2 * 60**2 - 42**2 } }{ 2 } = 42.298 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 60**2 - 29.33**2 } }{ 2 } = 49.668 ; ;
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