Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 0.545   b = 60   c = 59.45661463901

Area: T = 1.05551032399
Perimeter: p = 120.001114639
Semiperimeter: s = 60.00105731951

Angle ∠ A = α = 0.03438921877° = 0°2'2″ = 0.00105915303 rad
Angle ∠ B = β = 176.2666107812° = 176°15'58″ = 3.0766423941 rad
Angle ∠ C = γ = 3.7° = 3°42' = 0.06545771823 rad

Height: ha = 3.87219384952
Height: hb = 0.0355170108
Height: hc = 0.03554918138

Median: ma = 59.72880705827
Median: mb = 29.45661569843
Median: mc = 30.27219371136

Inradius: r = 0.0187584886
Circumradius: R = 460.676960864

Vertex coordinates: A[59.45661463901; 0] B[0; 0] C[-0.54438431126; 0.03554918138]
Centroid: CG[19.63774344258; 0.01218306046]
Coordinates of the circumscribed circle: U[29.72880731951; 459.7099397442]
Coordinates of the inscribed circle: I[0.00105731951; 0.0187584886]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.9666107812° = 179°57'58″ = 0.00105915303 rad
∠ B' = β' = 3.73438921877° = 3°44'2″ = 3.0766423941 rad
∠ C' = γ' = 176.3° = 176°18' = 0.06545771823 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 = 0.55 ; ; b = 60 ; ; gamma = 3° 42' ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 0.55**2+60**2 - 2 * 0.55 * 60 * cos(3° 42') } ; ; c = 59.46 ; ;


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 = 0.55 ; ; b = 60 ; ; c = 59.46 ; ;

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

p = a+b+c = 0.55+60+59.46 = 120 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 120 }{ 2 } = 60 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60 * (60-0.55)(60-60)(60-59.46) } ; ; T = sqrt{ 1.11 } = 1.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.06 }{ 0.55 } = 3.87 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.06 }{ 60 } = 0.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.06 }{ 59.46 } = 0.04 ; ;

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{ 0.55**2-60**2-59.46**2 }{ 2 * 60 * 59.46 } ) = 0° 2'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60**2-0.55**2-59.46**2 }{ 2 * 0.55 * 59.46 } ) = 176° 15'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 59.46**2-0.55**2-60**2 }{ 2 * 60 * 0.55 } ) = 3° 42' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.06 }{ 60 } = 0.02 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.55 }{ 2 * sin 0° 2'2" } = 460.67 ; ;




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