Triangle calculator SAS

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


Right isosceles triangle.

Sides: a = 200   b = 200   c = 282.8432712475

Area: T = 20000
Perimeter: p = 682.8432712475
Semiperimeter: s = 341.4211356237

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

Height: ha = 200
Height: hb = 200
Height: hc = 141.4211356237

Median: ma = 223.607679775
Median: mb = 223.607679775
Median: mc = 141.4211356237

Inradius: r = 58.57986437627
Circumradius: R = 141.4211356237

Vertex coordinates: A[282.8432712475; 0] B[0; 0] C[141.4211356237; 141.4211356237]
Centroid: CG[141.4211356237; 47.14404520791]
Coordinates of the circumscribed circle: U[141.4211356237; 0]
Coordinates of the inscribed circle: I[141.4211356237; 58.57986437627]

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 = 200 ; ; b = 200 ; ; gamma = 90° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 200**2+200**2 - 2 * 200 * 200 * cos(90° ) } ; ; c = 282.84 ; ;


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 = 200 ; ; b = 200 ; ; c = 282.84 ; ;

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

p = a+b+c = 200+200+282.84 = 682.84 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 682.84 }{ 2 } = 341.42 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 341.42 * (341.42-200)(341.42-200)(341.42-282.84) } ; ; T = sqrt{ 400000000 } = 20000 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 20000 }{ 200 } = 200 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 20000 }{ 200 } = 200 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 20000 }{ 282.84 } = 141.42 ; ;

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{ 200**2-200**2-282.84**2 }{ 2 * 200 * 282.84 } ) = 45° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 200**2-200**2-282.84**2 }{ 2 * 200 * 282.84 } ) = 45° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 282.84**2-200**2-200**2 }{ 2 * 200 * 200 } ) = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 20000 }{ 341.42 } = 58.58 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 200 }{ 2 * sin 45° } = 141.42 ; ;




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

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