Triangle calculator SSA

Please enter two sides and a non-included angle
°


Obtuse scalene triangle.

Sides: a = 3.5   b = 4.2   c = 0.77000888548

Area: T = 0.02113819117
Perimeter: p = 8.44000888548
Semiperimeter: s = 4.22000444274

Angle ∠ A = α = 0.83333204049° = 0°50' = 0.01545441848 rad
Angle ∠ B = β = 179° = 3.12441393611 rad
Angle ∠ C = γ = 0.16766795951° = 0°10' = 0.00329091077 rad

Height: ha = 0.01222182352
Height: hb = 0.01101818627
Height: hc = 0.06110834225

Median: ma = 2.45500126943
Median: mb = 1.44000222149
Median: mc = 3.85499959609

Inradius: r = 0.00550908775
Circumradius: R = 120.3277245847

Vertex coordinates: A[0.77000888548; 0] B[0; 0] C[-3.4999466933; 0.06110834225]
Centroid: CG[-0.93331260261; 0.02203611408]
Coordinates of the circumscribed circle: U[0.35500444274; 120.3276736688]
Coordinates of the inscribed circle: I[04.44274E-5; 0.00550908775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.1676679595° = 179°10' = 0.01545441848 rad
∠ B' = β' = 1° = 3.12441393611 rad
∠ C' = γ' = 179.8333320405° = 179°50' = 0.00329091077 rad

Calculate another triangle




How did we calculate this triangle?

1. Use Law of Cosines

a = 3.5 ; ; b = 4.2 ; ; beta = 179° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 4.2**2 = 3.5**2 + c**2 -2 * 4.2 * c * cos (179° ) ; ; ; ; c**2 +6.999c -5.39 =0 ; ; p=1; q=6.99893386609; r=-5.39 ; ; D = q**2 - 4pr = 6.999**2 - 4 * 1 * (-5.39) = 70.545075262 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ -7 ± sqrt{ 70.55 } }{ 2 } ; ; c_{1,2} = -3.49946693305 ± 4.19955578788 ; ; c_{1} = 0.70008885483 ; ;
c_{2} = -7.69902272092 ; ; ; ; (c -0.70008885483) (c +7.69902272092) = 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 = 0.7 ; ;

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

p = a+b+c = 3.5+4.2+0.7 = 8.4 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.4 }{ 2 } = 4.2 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.2 * (4.2-3.5)(4.2-4.2)(4.2-0.7) } ; ; T = sqrt{ 0 } = 0.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.02 }{ 3.5 } = 0.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.02 }{ 4.2 } = 0.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.02 }{ 0.7 } = 0.06 ; ;

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**2-0.7**2 }{ 2 * 4.2 * 0.7 } ) = 0° 50' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.2**2-3.5**2-0.7**2 }{ 2 * 3.5 * 0.7 } ) = 179° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.7**2-3.5**2-4.2**2 }{ 2 * 4.2 * 3.5 } ) = 0° 10' ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.02 }{ 4.2 } = 0.01 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.5 }{ 2 * sin 0° 50' } = 120.33 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.