Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 3.5   b = 4.2   c = 7.60326203573

Area: T = 2.31103170485
Perimeter: p = 15.30326203573
Semiperimeter: s = 7.65113101787

Angle ∠ A = α = 8.3220301852° = 8°19'13″ = 0.14552166621 rad
Angle ∠ B = β = 10° = 0.17545329252 rad
Angle ∠ C = γ = 161.6879698148° = 161°40'47″ = 2.82218430663 rad

Height: ha = 1.32201811705
Height: hb = 1.11001509755
Height: hc = 0.60877686218

Median: ma = 5.88770551338
Median: mb = 5.53330749271
Median: mc = 0.70435914479

Inradius: r = 0.30219505149
Circumradius: R = 12.09334180146

Vertex coordinates: A[7.60326203573; 0] B[0; 0] C[3.44768271355; 0.60877686218]
Centroid: CG[3.68331491643; 0.20325895406]
Coordinates of the circumscribed circle: U[3.80113101787; -11.48804529615]
Coordinates of the inscribed circle: I[3.45113101787; 0.30219505149]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.6879698148° = 171°40'47″ = 0.14552166621 rad
∠ B' = β' = 170° = 0.17545329252 rad
∠ C' = γ' = 18.3220301852° = 18°19'13″ = 2.82218430663 rad

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How did we calculate this triangle?

1. Use Law of Cosines

a = 3.5 ; ; b = 4.2 ; ; beta = 10° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 4.2**2 = 3.5**2 + c**2 -2 * 4.2 * c * cos (10° ) ; ; ; ; c**2 -6.894c -5.39 =0 ; ; p=1; q=-6.89365427109; r=-5.39 ; ; D = q**2 - 4pr = 6.894**2 - 4 * 1 * (-5.39) = 69.0824692093 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 6.89 ± sqrt{ 69.08 } }{ 2 } ; ; c_{1,2} = 3.44682713554 ± 4.15579322179 ; ; c_{1} = 7.60262035734 ; ;
c_{2} = -0.708966086252 ; ; ; ; (c -7.60262035734) (c +0.708966086252) = 0 ; ; ; ; c>0 ; ;


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 = 3.5 ; ; b = 4.2 ; ; c = 7.6 ; ;

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

p = a+b+c = 3.5+4.2+7.6 = 15.3 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 15.3 }{ 2 } = 7.65 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.65 * (7.65-3.5)(7.65-4.2)(7.65-7.6) } ; ; T = sqrt{ 5.34 } = 2.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.31 }{ 3.5 } = 1.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.31 }{ 4.2 } = 1.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.31 }{ 7.6 } = 0.61 ; ;

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{ 3.5**2-4.2**2-7.6**2 }{ 2 * 4.2 * 7.6 } ) = 8° 19'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.2**2-3.5**2-7.6**2 }{ 2 * 3.5 * 7.6 } ) = 10° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.6**2-3.5**2-4.2**2 }{ 2 * 4.2 * 3.5 } ) = 161° 40'47" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.31 }{ 7.65 } = 0.3 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.5 }{ 2 * sin 8° 19'13" } = 12.09 ; ;




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