Triangle calculator SAS

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


Right scalene triangle.

Sides: a = 2.8   b = 1.4   c = 3.13304951685

Area: T = 1.96
Perimeter: p = 7.33304951685
Semiperimeter: s = 3.66552475842

Angle ∠ A = α = 63.43549488229° = 63°26'6″ = 1.10771487178 rad
Angle ∠ B = β = 26.56550511771° = 26°33'54″ = 0.4643647609 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1.4
Height: hb = 2.8
Height: hc = 1.25221980674

Median: ma = 1.98798989873
Median: mb = 2.88661739379
Median: mc = 1.56552475842

Inradius: r = 0.53547524158
Circumradius: R = 1.56552475842

Vertex coordinates: A[3.13304951685; 0] B[0; 0] C[2.50443961348; 1.25221980674]
Centroid: CG[1.87882971011; 0.41773993558]
Coordinates of the circumscribed circle: U[1.56552475842; 0]
Coordinates of the inscribed circle: I[2.26552475842; 0.53547524158]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5655051177° = 116°33'54″ = 1.10771487178 rad
∠ B' = β' = 153.4354948823° = 153°26'6″ = 0.4643647609 rad
∠ C' = γ' = 90° = 1.57107963268 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 = 2.8 ; ; b = 1.4 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 2.8**2+1.4**2 - 2 * 2.8 * 1.4 * cos(90° ) } ; ; c = 3.13 ; ;


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 = 2.8 ; ; b = 1.4 ; ; c = 3.13 ; ;

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

p = a+b+c = 2.8+1.4+3.13 = 7.33 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.33 }{ 2 } = 3.67 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.67 * (3.67-2.8)(3.67-1.4)(3.67-3.13) } ; ; T = sqrt{ 3.84 } = 1.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.96 }{ 2.8 } = 1.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.96 }{ 1.4 } = 2.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.96 }{ 3.13 } = 1.25 ; ;

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{ 2.8**2-1.4**2-3.13**2 }{ 2 * 1.4 * 3.13 } ) = 63° 26'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.4**2-2.8**2-3.13**2 }{ 2 * 2.8 * 3.13 } ) = 26° 33'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.13**2-2.8**2-1.4**2 }{ 2 * 1.4 * 2.8 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.96 }{ 3.67 } = 0.53 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.8 }{ 2 * sin 63° 26'6" } = 1.57 ; ;




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

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