Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 49   b = 44   c = 36.13

Area: T = 766.5921701117
Perimeter: p = 129.13
Semiperimeter: s = 64.565

Angle ∠ A = α = 74.67436859326° = 74°40'25″ = 1.30333016841 rad
Angle ∠ B = β = 609.999871072° = 60° = 1.0477195301 rad
Angle ∠ C = γ = 45.32664429954° = 45°19'35″ = 0.79110956685 rad

Height: ha = 31.28994571885
Height: hb = 34.84550773235
Height: hc = 42.4355189655

Median: ma = 31.94443023089
Median: mb = 37.0032546534
Median: mc = 42.92203422051

Inradius: r = 11.87331774354
Circumradius: R = 25.40334448477

Vertex coordinates: A[36.13; 0] B[0; 0] C[24.55000954885; 42.4355189655]
Centroid: CG[20.21100318295; 14.14550632183]
Coordinates of the circumscribed circle: U[18.065; 17.86603131307]
Coordinates of the inscribed circle: I[20.565; 11.87331774354]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.3266314067° = 105°19'35″ = 1.30333016841 rad
∠ B' = β' = 1200.000128928° = 120° = 1.0477195301 rad
∠ C' = γ' = 134.6743557005° = 134°40'25″ = 0.79110956685 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 = 49+44+36.13 = 129.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 129.13 }{ 2 } = 64.57 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 64.57 * (64.57-49)(64.57-44)(64.57-36.13) } ; ; T = sqrt{ 587662.84 } = 766.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 766.59 }{ 49 } = 31.29 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 766.59 }{ 44 } = 34.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 766.59 }{ 36.13 } = 42.44 ; ;

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{ 44**2+36.13**2-49**2 }{ 2 * 44 * 36.13 } ) = 74° 40'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 49**2+36.13**2-44**2 }{ 2 * 49 * 36.13 } ) = 60° ; ;
 gamma = 180° - alpha - beta = 180° - 74° 40'25" - 60° = 45° 19'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 766.59 }{ 64.57 } = 11.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 49 }{ 2 * sin 74° 40'25" } = 25.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 44**2+2 * 36.13**2 - 49**2 } }{ 2 } = 31.944 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 36.13**2+2 * 49**2 - 44**2 } }{ 2 } = 37.003 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 44**2+2 * 49**2 - 36.13**2 } }{ 2 } = 42.92 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.