Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 2.75   b = 1.32   c = 1.8322445404

Area: T = 1.0411041232
Perimeter: p = 5.9022445404
Semiperimeter: s = 2.9511222702

Angle ∠ A = α = 120.596555085° = 120°35'44″ = 2.10547894256 rad
Angle ∠ B = β = 24.40444491499° = 24°24'16″ = 0.42659379898 rad
Angle ∠ C = γ = 35° = 0.61108652382 rad

Height: ha = 0.7577120896
Height: hb = 1.57773352
Height: hc = 1.13662316495

Median: ma = 0.81220979493
Median: mb = 2.24215570658
Median: mc = 1.95326868567

Inradius: r = 0.35327491271
Circumradius: R = 1.59773855338

Vertex coordinates: A[1.8322445404; 0] B[0; 0] C[2.50442918437; 1.13662316495]
Centroid: CG[1.44655790826; 0.37987438832]
Coordinates of the circumscribed circle: U[0.9166222702; 1.30985016256]
Coordinates of the inscribed circle: I[1.6311222702; 0.35327491271]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 59.40444491499° = 59°24'16″ = 2.10547894256 rad
∠ B' = β' = 155.596555085° = 155°35'44″ = 0.42659379898 rad
∠ C' = γ' = 145° = 0.61108652382 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 = 2.75 ; ; b = 1.32 ; ; gamma = 35° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 2.75**2+1.32**2 - 2 * 2.75 * 1.32 * cos(35° ) } ; ; c = 1.83 ; ;


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 = 2.75 ; ; b = 1.32 ; ; c = 1.83 ; ;

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

p = a+b+c = 2.75+1.32+1.83 = 5.9 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.9 }{ 2 } = 2.95 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.95 * (2.95-2.75)(2.95-1.32)(2.95-1.83) } ; ; T = sqrt{ 1.08 } = 1.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.04 }{ 2.75 } = 0.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.04 }{ 1.32 } = 1.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.04 }{ 1.83 } = 1.14 ; ;

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{ 2.75**2-1.32**2-1.83**2 }{ 2 * 1.32 * 1.83 } ) = 120° 35'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.32**2-2.75**2-1.83**2 }{ 2 * 2.75 * 1.83 } ) = 24° 24'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.83**2-2.75**2-1.32**2 }{ 2 * 1.32 * 2.75 } ) = 35° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.04 }{ 2.95 } = 0.35 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.75 }{ 2 * sin 120° 35'44" } = 1.6 ; ;




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