Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 35   b = 33   c = 34.14

Area: T = 501.07700244
Perimeter: p = 102.14
Semiperimeter: s = 51.07

Angle ∠ A = α = 62.81217707189° = 62°48'42″ = 1.09662722081 rad
Angle ∠ B = β = 57.0011108196° = 57°4″ = 0.99548570153 rad
Angle ∠ C = γ = 60.18771210851° = 60°11'14″ = 1.05504634302 rad

Height: ha = 28.63325728228
Height: hb = 30.36878802667
Height: hc = 29.35438385706

Median: ma = 28.65334430741
Median: mb = 30.38112409226
Median: mc = 29.42113374951

Inradius: r = 9.81114357627
Circumradius: R = 19.67437472209

Vertex coordinates: A[34.14; 0] B[0; 0] C[19.06217984769; 29.35438385706]
Centroid: CG[17.73439328256; 9.78546128569]
Coordinates of the circumscribed circle: U[17.07; 9.78111773172]
Coordinates of the inscribed circle: I[18.07; 9.81114357627]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.1888229281° = 117°11'18″ = 1.09662722081 rad
∠ B' = β' = 122.9998891804° = 122°59'56″ = 0.99548570153 rad
∠ C' = γ' = 119.8132878915° = 119°48'46″ = 1.05504634302 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 = 35+33+34.14 = 102.14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 102.14 }{ 2 } = 51.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 51.07 * (51.07-35)(51.07-33)(51.07-34.14) } ; ; T = sqrt{ 251071.17 } = 501.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 501.07 }{ 35 } = 28.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 501.07 }{ 33 } = 30.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 501.07 }{ 34.14 } = 29.35 ; ;

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{ 33**2+34.14**2-35**2 }{ 2 * 33 * 34.14 } ) = 62° 48'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+34.14**2-33**2 }{ 2 * 35 * 34.14 } ) = 57° 4" ; ; gamma = 180° - alpha - beta = 180° - 62° 48'42" - 57° 4" = 60° 11'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 501.07 }{ 51.07 } = 9.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 62° 48'42" } = 19.67 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 34.14**2 - 35**2 } }{ 2 } = 28.653 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 34.14**2+2 * 35**2 - 33**2 } }{ 2 } = 30.381 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 35**2 - 34.14**2 } }{ 2 } = 29.421 ; ;
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