Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°


Acute scalene triangle.

Sides: a = 110   b = 130   c = 80.39221168203

Area: T = 4401.987954858
Perimeter: p = 320.392211682
Semiperimeter: s = 160.196605841

Angle ∠ A = α = 57.39550142762° = 57°23'42″ = 1.00217319733 rad
Angle ∠ B = β = 84.60549857238° = 84°36'18″ = 1.47766355645 rad
Angle ∠ C = γ = 38° = 0.66332251158 rad

Height: ha = 80.03659917923
Height: hb = 67.72327622858
Height: hc = 109.5132716487

Median: ma = 93.04400248464
Median: mb = 71.10986930229
Median: mc = 113.5098928672

Inradius: r = 27.47987007387
Circumradius: R = 65.28992214652

Vertex coordinates: A[80.39221168203; 0] B[0; 0] C[10.34223850038; 109.5132716487]
Centroid: CG[30.24548339414; 36.50442388291]
Coordinates of the circumscribed circle: U[40.19660584101; 51.44986086092]
Coordinates of the inscribed circle: I[30.19660584101; 27.47987007387]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.6054985724° = 122°36'18″ = 1.00217319733 rad
∠ B' = β' = 95.39550142762° = 95°23'42″ = 1.47766355645 rad
∠ C' = γ' = 142° = 0.66332251158 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculation of the third side c of the triangle using a Law of Cosines

a = 110 ; ; b = 130 ; ; gamma = 38° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 110**2+130**2 - 2 * 110 * 130 * cos(38° ) } ; ; c = 80.39 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 110 ; ; b = 130 ; ; c = 80.39 ; ;

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

p = a+b+c = 110+130+80.39 = 320.39 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 320.39 }{ 2 } = 160.2 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 160.2 * (160.2-110)(160.2-130)(160.2-80.39) } ; ; T = sqrt{ 19377423.95 } = 4401.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4401.98 }{ 110 } = 80.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4401.98 }{ 130 } = 67.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4401.98 }{ 80.39 } = 109.51 ; ;

6. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 110**2-130**2-80.39**2 }{ 2 * 130 * 80.39 } ) = 57° 23'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 130**2-110**2-80.39**2 }{ 2 * 110 * 80.39 } ) = 84° 36'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 80.39**2-110**2-130**2 }{ 2 * 130 * 110 } ) = 38° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4401.98 }{ 160.2 } = 27.48 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 110 }{ 2 * sin 57° 23'42" } = 65.29 ; ;




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

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