Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 99.43   b = 105.71   c = 50

Area: T = 2467.222239703
Perimeter: p = 255.14
Semiperimeter: s = 127.57

Angle ∠ A = α = 699.0001648508° = 69°1″ = 1.20442800611 rad
Angle ∠ B = β = 833.0001514212° = 83°1″ = 1.4498625922 rad
Angle ∠ C = γ = 287.9996837281° = 27°59'59″ = 0.48986866706 rad

Height: ha = 49.62773236857
Height: hb = 46.67990728793
Height: hc = 98.68988958814

Median: ma = 66.07436015743
Median: mb = 58.30553293019
Median: mc = 99.52662000681

Inradius: r = 19.34401457791
Circumradius: R = 53.25219145448

Vertex coordinates: A[50; 0] B[0; 0] C[12.1177208; 98.68988958814]
Centroid: CG[20.7065736; 32.89662986271]
Coordinates of the circumscribed circle: U[25; 47.01987877629]
Coordinates of the inscribed circle: I[21.86; 19.34401457791]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1110.999835149° = 110°59'59″ = 1.20442800611 rad
∠ B' = β' = 976.9998485788° = 96°59'59″ = 1.4498625922 rad
∠ C' = γ' = 1522.000316272° = 152°1″ = 0.48986866706 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 = 99.43+105.71+50 = 255.14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 255.14 }{ 2 } = 127.57 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 127.57 * (127.57-99.43)(127.57-105.71)(127.57-50) } ; ; T = sqrt{ 6087186.36 } = 2467.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2467.22 }{ 99.43 } = 49.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2467.22 }{ 105.71 } = 46.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2467.22 }{ 50 } = 98.69 ; ;

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{ 105.71**2+50**2-99.43**2 }{ 2 * 105.71 * 50 } ) = 69° 1" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 99.43**2+50**2-105.71**2 }{ 2 * 99.43 * 50 } ) = 83° 1" ; ; gamma = 180° - alpha - beta = 180° - 69° 1" - 83° 1" = 27° 59'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2467.22 }{ 127.57 } = 19.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 99.43 }{ 2 * sin 69° 1" } = 53.25 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 105.71**2+2 * 50**2 - 99.43**2 } }{ 2 } = 66.074 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 99.43**2 - 105.71**2 } }{ 2 } = 58.305 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 105.71**2+2 * 99.43**2 - 50**2 } }{ 2 } = 99.526 ; ;
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