Triangle calculator SAS

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


Obtuse scalene triangle.

Sides: a = 2.327   b = 2.853   c = 1.6366444377

Area: T = 1.90439671921
Perimeter: p = 6.8166444377
Semiperimeter: s = 3.40882221885

Angle ∠ A = α = 54.64884463084° = 54°38'54″ = 0.95437953192 rad
Angle ∠ B = β = 90.35215536916° = 90°21'6″ = 1.57769320962 rad
Angle ∠ C = γ = 35° = 0.61108652382 rad

Height: ha = 1.63664135729
Height: hb = 1.33547123674
Height: hc = 2.32769561971

Median: ma = 2.01437148133
Median: mb = 1.41882867656
Median: mc = 2.47113926135

Inradius: r = 0.55986393981
Circumradius: R = 1.42765268526

Vertex coordinates: A[1.6366444377; 0] B[0; 0] C[-0.01442778458; 2.32769561971]
Centroid: CG[0.5410722177; 0.77656520657]
Coordinates of the circumscribed circle: U[0.81882221885; 1.16985423876]
Coordinates of the inscribed circle: I[0.55552221885; 0.55986393981]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.3521553692° = 125°21'6″ = 0.95437953192 rad
∠ B' = β' = 89.64884463084° = 89°38'54″ = 1.57769320962 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 = 2.33 ; ; b = 2.85 ; ; gamma = 35° ; ; ; ; c**2 = a**2+b**2 - 2ab cos( gamma ) ; ; c = sqrt{ a**2+b**2 - 2ab cos( gamma ) } ; ; c = sqrt{ 2.33**2+2.85**2 - 2 * 2.33 * 2.85 * cos(35° ) } ; ; c = 1.64 ; ;


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 = 2.33 ; ; b = 2.85 ; ; c = 1.64 ; ;

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

p = a+b+c = 2.33+2.85+1.64 = 6.82 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.82 }{ 2 } = 3.41 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.41 * (3.41-2.33)(3.41-2.85)(3.41-1.64) } ; ; T = sqrt{ 3.63 } = 1.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.9 }{ 2.33 } = 1.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.9 }{ 2.85 } = 1.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.9 }{ 1.64 } = 2.33 ; ;

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{ 2.33**2-2.85**2-1.64**2 }{ 2 * 2.85 * 1.64 } ) = 54° 38'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.85**2-2.33**2-1.64**2 }{ 2 * 2.33 * 1.64 } ) = 90° 21'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.64**2-2.33**2-2.85**2 }{ 2 * 2.85 * 2.33 } ) = 35° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.9 }{ 3.41 } = 0.56 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.33 }{ 2 * sin 54° 38'54" } = 1.43 ; ;




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