Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 2000   b = 1700   c = 3499.782186813

Area: T = 1046624.508805
Perimeter: p = 7199.782186813
Semiperimeter: s = 3599.891093407

Angle ∠ A = α = 20.59991942438° = 20°35'57″ = 0.36595237628 rad
Angle ∠ B = β = 17.40108057562° = 17°24'3″ = 0.30437013529 rad
Angle ∠ C = γ = 142° = 2.47883675378 rad

Height: ha = 1046.625450805
Height: hb = 1231.323295065
Height: hc = 598.1088423604

Median: ma = 2563.052219655
Median: mb = 2720.613326952
Median: mc = 618.7744368303

Inradius: r = 290.7387838235
Circumradius: R = 2842.294402715

Vertex coordinates: A[3499.782186813; 0] B[0; 0] C[1908.472224596; 598.1088423604]
Centroid: CG[1802.751137137; 199.3699474535]
Coordinates of the circumscribed circle: U[1749.891093407; -2239.758825831]
Coordinates of the inscribed circle: I[1899.891093407; 290.7387838235]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.4010805756° = 159°24'3″ = 0.36595237628 rad
∠ B' = β' = 162.5999194244° = 162°35'57″ = 0.30437013529 rad
∠ C' = γ' = 38° = 2.47883675378 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 = 2000 ; ; b = 1700 ; ; gamma = 142° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 2000**2+1700**2 - 2 * 2000 * 1700 * cos(142° ) } ; ; c = 3499.78 ; ;


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 = 2000 ; ; b = 1700 ; ; c = 3499.78 ; ;

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

p = a+b+c = 2000+1700+3499.78 = 7199.78 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7199.78 }{ 2 } = 3599.89 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3599.89 * (3599.89-2000)(3599.89-1700)(3599.89-3499.78) } ; ; T = sqrt{ 1.095 * 10**{ 12 } } = 1046624.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1046624.51 }{ 2000 } = 1046.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1046624.51 }{ 1700 } = 1231.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1046624.51 }{ 3499.78 } = 598.11 ; ;

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{ 2000**2-1700**2-3499.78**2 }{ 2 * 1700 * 3499.78 } ) = 20° 35'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1700**2-2000**2-3499.78**2 }{ 2 * 2000 * 3499.78 } ) = 17° 24'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3499.78**2-2000**2-1700**2 }{ 2 * 1700 * 2000 } ) = 142° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1046624.51 }{ 3599.89 } = 290.74 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2000 }{ 2 * sin 20° 35'57" } = 2842.29 ; ;




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