Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=7.78797870838 and with side c=1.43106304119

#1 Acute scalene triangle.

Sides: a = 8.3   b = 7.6   c = 7.78797870838

Area: T = 26.86105676245
Perimeter: p = 23.68797870838
Semiperimeter: s = 11.84398935419

Angle ∠ A = α = 65.31100521554° = 65°18'36″ = 1.14398754448 rad
Angle ∠ B = β = 56.3° = 56°18' = 0.98326203689 rad
Angle ∠ C = γ = 58.39899478446° = 58°23'24″ = 1.019909684 rad

Height: ha = 6.47224259336
Height: hb = 7.06985704275
Height: hc = 6.90552192137

Median: ma = 6.47545689844
Median: mb = 7.09899607569
Median: mc = 6.94221702826

Inradius: r = 2.26986494207
Circumradius: R = 4.56875595552

Vertex coordinates: A[7.78797870838; 0] B[0; 0] C[4.60552087478; 6.90552192137]
Centroid: CG[4.12883319439; 2.30217397379]
Coordinates of the circumscribed circle: U[3.89898935419; 2.39440193238]
Coordinates of the inscribed circle: I[4.24398935419; 2.26986494207]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.6989947845° = 114°41'24″ = 1.14398754448 rad
∠ B' = β' = 123.7° = 123°42' = 0.98326203689 rad
∠ C' = γ' = 121.6110052155° = 121°36'36″ = 1.019909684 rad




How did we calculate this triangle?

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 = 8.3 ; ; b = 7.6 ; ; c = 7.78 ; ;

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

p = a+b+c = 8.3+7.6+7.78 = 23.68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.68 }{ 2 } = 11.84 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.84 * (11.84-8.3)(11.84-7.6)(11.84-7.78) } ; ; T = sqrt{ 721.49 } = 26.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.86 }{ 8.3 } = 6.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.86 }{ 7.6 } = 7.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.86 }{ 7.78 } = 6.91 ; ;

5. 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{ 8.3**2-7.6**2-7.78**2 }{ 2 * 7.6 * 7.78 } ) = 65° 18'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.6**2-8.3**2-7.78**2 }{ 2 * 8.3 * 7.78 } ) = 56° 18' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.78**2-8.3**2-7.6**2 }{ 2 * 7.6 * 8.3 } ) = 58° 23'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.86 }{ 11.84 } = 2.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.3 }{ 2 * sin 65° 18'36" } = 4.57 ; ;





#2 Obtuse scalene triangle.

Sides: a = 8.3   b = 7.6   c = 1.43106304119

Area: T = 4.93994083039
Perimeter: p = 17.33106304119
Semiperimeter: s = 8.66553152059

Angle ∠ A = α = 114.6989947845° = 114°41'24″ = 2.00217172088 rad
Angle ∠ B = β = 56.3° = 56°18' = 0.98326203689 rad
Angle ∠ C = γ = 9.01100521554° = 9°36″ = 0.15772550759 rad

Height: ha = 1.19902188684
Height: hb = 1.32998442905
Height: hc = 6.90552192137

Median: ma = 3.56110183498
Median: mb = 4.58656680743
Median: mc = 7.92554857363

Inradius: r = 0.57700206151
Circumradius: R = 4.56875595552

Vertex coordinates: A[1.43106304119; 0] B[0; 0] C[4.60552087478; 6.90552192137]
Centroid: CG[2.01219463866; 2.30217397379]
Coordinates of the circumscribed circle: U[0.71553152059; 4.51111998898]
Coordinates of the inscribed circle: I[1.06553152059; 0.57700206151]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 65.31100521554° = 65°18'36″ = 2.00217172088 rad
∠ B' = β' = 123.7° = 123°42' = 0.98326203689 rad
∠ C' = γ' = 170.9989947845° = 170°59'24″ = 0.15772550759 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 8.3 ; ; b = 7.6 ; ; beta = 56° 18' ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 7.6**2 = 8.3**2 + c**2 -2 * 7.6 * c * cos (56° 18') ; ; ; ; c**2 -9.21c +11.13 =0 ; ; p=1; q=-9.21041749564; r=11.13 ; ; D = q**2 - 4pr = 9.21**2 - 4 * 1 * 11.13 = 40.3117904439 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 9.21 ± sqrt{ 40.31 } }{ 2 } ; ; c_{1,2} = 4.60520874782 ± 3.17457833593 ; ;
c_{1} = 7.77978708375 ; ; c_{2} = 1.43063041188 ; ; ; ; (c -7.77978708375) (c -1.43063041188) = 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 = 8.3 ; ; b = 7.6 ; ; c = 1.43 ; ;

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

p = a+b+c = 8.3+7.6+1.43 = 17.33 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.33 }{ 2 } = 8.67 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.67 * (8.67-8.3)(8.67-7.6)(8.67-1.43) } ; ; T = sqrt{ 24.4 } = 4.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.94 }{ 8.3 } = 1.19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.94 }{ 7.6 } = 1.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.94 }{ 1.43 } = 6.91 ; ;

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{ 8.3**2-7.6**2-1.43**2 }{ 2 * 7.6 * 1.43 } ) = 114° 41'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.6**2-8.3**2-1.43**2 }{ 2 * 8.3 * 1.43 } ) = 56° 18' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.43**2-8.3**2-7.6**2 }{ 2 * 7.6 * 8.3 } ) = 9° 36" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.94 }{ 8.67 } = 0.57 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.3 }{ 2 * sin 114° 41'24" } = 4.57 ; ;




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

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