Triangle calculator SAS

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


Obtuse isosceles triangle.

Sides: a = 70   b = 70   c = 121.244355653

Area: T = 2121.762223927
Perimeter: p = 261.244355653
Semiperimeter: s = 130.6221778265

Angle ∠ A = α = 30° = 0.52435987756 rad
Angle ∠ B = β = 30° = 0.52435987756 rad
Angle ∠ C = γ = 120° = 2.09443951024 rad

Height: ha = 60.62217782649
Height: hb = 60.62217782649
Height: hc = 35

Median: ma = 92.60112958873
Median: mb = 92.60112958873
Median: mc = 35

Inradius: r = 16.24435565298
Circumradius: R = 70

Vertex coordinates: A[121.244355653; 0] B[0; 0] C[60.62217782649; 35]
Centroid: CG[60.62217782649; 11.66766666667]
Coordinates of the circumscribed circle: U[60.62217782649; -35]
Coordinates of the inscribed circle: I[60.62217782649; 16.24435565298]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150° = 0.52435987756 rad
∠ B' = β' = 150° = 0.52435987756 rad
∠ C' = γ' = 60° = 2.09443951024 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 = 70 ; ; b = 70 ; ; gamma = 120° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 70**2+70**2 - 2 * 70 * 70 * cos(120° ) } ; ; c = 121.24 ; ;


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 = 70 ; ; b = 70 ; ; c = 121.24 ; ;

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

p = a+b+c = 70+70+121.24 = 261.24 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 261.24 }{ 2 } = 130.62 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 130.62 * (130.62-70)(130.62-70)(130.62-121.24) } ; ; T = sqrt{ 4501875 } = 2121.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2121.76 }{ 70 } = 60.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2121.76 }{ 70 } = 60.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2121.76 }{ 121.24 } = 35 ; ;

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{ 70**2-70**2-121.24**2 }{ 2 * 70 * 121.24 } ) = 30° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 70**2-70**2-121.24**2 }{ 2 * 70 * 121.24 } ) = 30° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 121.24**2-70**2-70**2 }{ 2 * 70 * 70 } ) = 120° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2121.76 }{ 130.62 } = 16.24 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 70 }{ 2 * sin 30° } = 70 ; ;




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

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