Triangle calculator SAS

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


Obtuse isosceles triangle.

Sides: a = 1.14   b = 1.14   c = 2.23301765297

Area: T = 0.26442974707
Perimeter: p = 4.51101765297
Semiperimeter: s = 2.25550882648

Angle ∠ A = α = 12° = 0.20994395102 rad
Angle ∠ B = β = 12° = 0.20994395102 rad
Angle ∠ C = γ = 156° = 2.72327136331 rad

Height: ha = 0.46436797731
Height: hb = 0.46436797731
Height: hc = 0.23770193275

Median: ma = 1.67768254759
Median: mb = 1.67768254759
Median: mc = 0.23770193275

Inradius: r = 0.11772004993
Circumradius: R = 2.74215485765

Vertex coordinates: A[2.23301765297; 0] B[0; 0] C[1.11550882648; 0.23770193275]
Centroid: CG[1.11550882648; 0.07990064425]
Coordinates of the circumscribed circle: U[1.11550882648; -2.5054529249]
Coordinates of the inscribed circle: I[1.11550882648; 0.11772004993]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168° = 0.20994395102 rad
∠ B' = β' = 168° = 0.20994395102 rad
∠ C' = γ' = 24° = 2.72327136331 rad

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How did we calculate this triangle?

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

a = 1.14 ; ; b = 1.14 ; ; gamma = 156° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 1.14**2+1.14**2 - 2 * 1.14 * 1.14 * cos(156° ) } ; ; c = 2.23 ; ;


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 = 1.14 ; ; b = 1.14 ; ; c = 2.23 ; ;

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

p = a+b+c = 1.14+1.14+2.23 = 4.51 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4.51 }{ 2 } = 2.26 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.26 * (2.26-1.14)(2.26-1.14)(2.26-2.23) } ; ; T = sqrt{ 0.07 } = 0.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.26 }{ 1.14 } = 0.46 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.26 }{ 1.14 } = 0.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.26 }{ 2.23 } = 0.24 ; ;

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{ 1.14**2-1.14**2-2.23**2 }{ 2 * 1.14 * 2.23 } ) = 12° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.14**2-1.14**2-2.23**2 }{ 2 * 1.14 * 2.23 } ) = 12° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.23**2-1.14**2-1.14**2 }{ 2 * 1.14 * 1.14 } ) = 156° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.26 }{ 2.26 } = 0.12 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.14 }{ 2 * sin 12° } = 2.74 ; ;




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