Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 38   b = 120   c = 125.87

Area: T = 22809.99999243
Perimeter: p = 283.87
Semiperimeter: s = 141.935

Angle ∠ A = α = 17.57216842119° = 17°34'18″ = 0.30766837446 rad
Angle ∠ B = β = 72.43329842633° = 72°25'59″ = 1.26441940624 rad
Angle ∠ C = γ = 89.99553315248° = 89°59'43″ = 1.57107148465 rad

Height: ha = 1209.999999602
Height: hb = 387.9999998739
Height: hc = 36.2287854015

Median: ma = 121.4933326771
Median: mb = 71.0198507799
Median: mc = 62.93879517859

Inradius: r = 16.06436910729
Circumradius: R = 62.93550002089

Vertex coordinates: A[125.87; 0] B[0; 0] C[11.46992019544; 36.2287854015]
Centroid: CG[45.78797339848; 12.07659513383]
Coordinates of the circumscribed circle: U[62.935; 0.00551279604]
Coordinates of the inscribed circle: I[21.935; 16.06436910729]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.4288315788° = 162°25'42″ = 0.30766837446 rad
∠ B' = β' = 107.5677015737° = 107°34'1″ = 1.26441940624 rad
∠ C' = γ' = 90.00546684752° = 90°17″ = 1.57107148465 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 = 38+120+125.87 = 283.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 283.87 }{ 2 } = 141.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 141.94 * (141.94-38)(141.94-120)(141.94-125.87) } ; ; T = sqrt{ 5198399.97 } = 2280 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2280 }{ 38 } = 120 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2280 }{ 120 } = 38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2280 }{ 125.87 } = 36.23 ; ;

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{ 120**2+125.87**2-38**2 }{ 2 * 120 * 125.87 } ) = 17° 34'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38**2+125.87**2-120**2 }{ 2 * 38 * 125.87 } ) = 72° 25'59" ; ; gamma = 180° - alpha - beta = 180° - 17° 34'18" - 72° 25'59" = 89° 59'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2280 }{ 141.94 } = 16.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38 }{ 2 * sin 17° 34'18" } = 62.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 120**2+2 * 125.87**2 - 38**2 } }{ 2 } = 121.493 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 125.87**2+2 * 38**2 - 120**2 } }{ 2 } = 71.019 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 120**2+2 * 38**2 - 125.87**2 } }{ 2 } = 62.938 ; ;
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