Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 74.12   b = 75.19   c = 105.58

Area: T = 2786.541139966
Perimeter: p = 254.89
Semiperimeter: s = 127.445

Angle ∠ A = α = 44.59898494399° = 44°35'23″ = 0.77882396857 rad
Angle ∠ B = β = 45.41110455042° = 45°24'40″ = 0.79325722608 rad
Angle ∠ C = γ = 89.99991050559° = 89°59'57″ = 1.57107807071 rad

Height: ha = 75.19899999908
Height: hb = 74.1219999991
Height: hc = 52.78554025319

Median: ma = 83.82765629142
Median: mb = 83.10987924049
Median: mc = 52.79108244868

Inradius: r = 21.86546584775
Circumradius: R = 52.79900000064

Vertex coordinates: A[105.58; 0] B[0; 0] C[52.03334092631; 52.78554025319]
Centroid: CG[52.53878030877; 17.59551341773]
Coordinates of the circumscribed circle: U[52.79; 0.00108245651]
Coordinates of the inscribed circle: I[52.255; 21.86546584775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.411015056° = 135°24'37″ = 0.77882396857 rad
∠ B' = β' = 134.5898954496° = 134°35'20″ = 0.79325722608 rad
∠ C' = γ' = 90.00108949441° = 90°3″ = 1.57107807071 rad

Calculate another triangle


How did we calculate this triangle?

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

p = a+b+c = 74.12+75.19+105.58 = 254.89 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 254.89 }{ 2 } = 127.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 127.45 * (127.45-74.12)(127.45-75.19)(127.45-105.58) } ; ; T = sqrt{ 7764812.97 } = 2786.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2786.54 }{ 74.12 } = 75.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2786.54 }{ 75.19 } = 74.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2786.54 }{ 105.58 } = 52.79 ; ;

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{ 75.19**2+105.58**2-74.12**2 }{ 2 * 75.19 * 105.58 } ) = 44° 35'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 74.12**2+105.58**2-75.19**2 }{ 2 * 74.12 * 105.58 } ) = 45° 24'40" ; ; gamma = 180° - alpha - beta = 180° - 44° 35'23" - 45° 24'40" = 89° 59'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2786.54 }{ 127.45 } = 21.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 74.12 }{ 2 * sin 44° 35'23" } = 52.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 75.19**2+2 * 105.58**2 - 74.12**2 } }{ 2 } = 83.827 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 105.58**2+2 * 74.12**2 - 75.19**2 } }{ 2 } = 83.109 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 75.19**2+2 * 74.12**2 - 105.58**2 } }{ 2 } = 52.791 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.