Triangle calculator SAS

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


Right isosceles triangle.

Sides: a = 120   b = 120   c = 169.7065627485

Area: T = 7200
Perimeter: p = 409.7065627485
Semiperimeter: s = 204.8532813742

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 120
Height: hb = 120
Height: hc = 84.85328137424

Median: ma = 134.164407865
Median: mb = 134.164407865
Median: mc = 84.85328137424

Inradius: r = 35.14771862576
Circumradius: R = 84.85328137424

Vertex coordinates: A[169.7065627485; 0] B[0; 0] C[84.85328137424; 84.85328137424]
Centroid: CG[84.85328137424; 28.28442712475]
Coordinates of the circumscribed circle: U[84.85328137424; -0]
Coordinates of the inscribed circle: I[84.85328137424; 35.14771862576]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 135° = 0.78553981634 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 = 120 ; ; b = 120 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos gamma ; ; c = sqrt{ a**2+b**2 - 2ab cos gamma } ; ; c = sqrt{ 120**2+120**2 - 2 * 120 * 120 * cos 90° } ; ; c = 169.71 ; ;
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 = 120 ; ; b = 120 ; ; c = 169.71 ; ;

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

p = a+b+c = 120+120+169.71 = 409.71 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 409.71 }{ 2 } = 204.85 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 204.85 * (204.85-120)(204.85-120)(204.85-169.71) } ; ; T = sqrt{ 51840000 } = 7200 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7200 }{ 120 } = 120 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7200 }{ 120 } = 120 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7200 }{ 169.71 } = 84.85 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 120**2+169.71**2-120**2 }{ 2 * 120 * 169.71 } ) = 45° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 120**2+169.71**2-120**2 }{ 2 * 120 * 169.71 } ) = 45° ; ; gamma = 180° - alpha - beta = 180° - 45° - 45° = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7200 }{ 204.85 } = 35.15 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 120 }{ 2 * sin 45° } = 84.85 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 120**2+2 * 169.71**2 - 120**2 } }{ 2 } = 134.164 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 169.71**2+2 * 120**2 - 120**2 } }{ 2 } = 134.164 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 120**2+2 * 120**2 - 169.71**2 } }{ 2 } = 84.853 ; ;
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.