Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=11.15985157139 and with side c=1.1654859228

#1 Obtuse scalene triangle.

Sides: a = 6.41   b = 5.3   c = 11.15985157139

Area: T = 9.85876305708
Perimeter: p = 22.86985157139
Semiperimeter: s = 11.4344257857

Angle ∠ A = α = 19.47331559742° = 19°28'23″ = 0.34398706875 rad
Angle ∠ B = β = 16° = 0.27992526803 rad
Angle ∠ C = γ = 144.5276844026° = 144°31'37″ = 2.52224692858 rad

Height: ha = 3.07657037662
Height: hb = 3.72198605927
Height: hc = 1.76768354508

Median: ma = 8.12658360474
Median: mb = 8.70550437373
Median: mc = 1.8660357967

Inradius: r = 0.86221137195
Circumradius: R = 9.61440814881

Vertex coordinates: A[11.15985157139; 0] B[0; 0] C[6.1621687471; 1.76768354508]
Centroid: CG[5.77334010616; 0.58989451503]
Coordinates of the circumscribed circle: U[5.5799257857; -7.83295877686]
Coordinates of the inscribed circle: I[6.1344257857; 0.86221137195]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.5276844026° = 160°31'37″ = 0.34398706875 rad
∠ B' = β' = 164° = 0.27992526803 rad
∠ C' = γ' = 35.47331559742° = 35°28'23″ = 2.52224692858 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 = 6.41 ; ; b = 5.3 ; ; c = 11.16 ; ;

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

p = a+b+c = 6.41+5.3+11.16 = 22.87 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.87 }{ 2 } = 11.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.43 * (11.43-6.41)(11.43-5.3)(11.43-11.16) } ; ; T = sqrt{ 97.17 } = 9.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 9.86 }{ 6.41 } = 3.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 9.86 }{ 5.3 } = 3.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 9.86 }{ 11.16 } = 1.77 ; ;

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{ 6.41**2-5.3**2-11.16**2 }{ 2 * 5.3 * 11.16 } ) = 19° 28'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.3**2-6.41**2-11.16**2 }{ 2 * 6.41 * 11.16 } ) = 16° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.16**2-6.41**2-5.3**2 }{ 2 * 5.3 * 6.41 } ) = 144° 31'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 9.86 }{ 11.43 } = 0.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.41 }{ 2 * sin 19° 28'23" } = 9.61 ; ;





#2 Obtuse scalene triangle.

Sides: a = 6.41   b = 5.3   c = 1.1654859228

Area: T = 1.02990572896
Perimeter: p = 12.8754859228
Semiperimeter: s = 6.4377429614

Angle ∠ A = α = 160.5276844026° = 160°31'37″ = 2.80217219661 rad
Angle ∠ B = β = 16° = 0.27992526803 rad
Angle ∠ C = γ = 3.47331559742° = 3°28'23″ = 0.06106180072 rad

Height: ha = 0.32110787175
Height: hb = 0.38883235055
Height: hc = 1.76768354508

Median: ma = 2.11098396883
Median: mb = 3.76882885386
Median: mc = 5.85223350677

Inradius: r = 0.16598553074
Circumradius: R = 9.61440814881

Vertex coordinates: A[1.1654859228; 0] B[0; 0] C[6.1621687471; 1.76768354508]
Centroid: CG[2.4422182233; 0.58989451503]
Coordinates of the circumscribed circle: U[0.5822429614; 9.59664232194]
Coordinates of the inscribed circle: I[1.1377429614; 0.16598553074]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 19.47331559742° = 19°28'23″ = 2.80217219661 rad
∠ B' = β' = 164° = 0.27992526803 rad
∠ C' = γ' = 176.5276844026° = 176°31'37″ = 0.06106180072 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 6.41 ; ; b = 5.3 ; ; beta = 16° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 5.3**2 = 6.41**2 + c**2 -2 * 5.3 * c * cos (16° ) ; ; ; ; c**2 -12.323c +12.998 =0 ; ; p=1; q=-12.3233749419; r=12.9981 ; ; D = q**2 - 4pr = 12.323**2 - 4 * 1 * 12.998 = 99.8731699594 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 12.32 ± sqrt{ 99.87 } }{ 2 } ; ; c_{1,2} = 6.16168747096 ± 4.99682824298 ; ;
c_{1} = 11.1585157139 ; ; c_{2} = 1.16485922798 ; ; ; ; (c -11.1585157139) (c -1.16485922798) = 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 = 6.41 ; ; b = 5.3 ; ; c = 1.16 ; ;

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

p = a+b+c = 6.41+5.3+1.16 = 12.87 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.87 }{ 2 } = 6.44 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.44 * (6.44-6.41)(6.44-5.3)(6.44-1.16) } ; ; T = sqrt{ 1.06 } = 1.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.03 }{ 6.41 } = 0.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.03 }{ 5.3 } = 0.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.03 }{ 1.16 } = 1.77 ; ;

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{ 6.41**2-5.3**2-1.16**2 }{ 2 * 5.3 * 1.16 } ) = 160° 31'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.3**2-6.41**2-1.16**2 }{ 2 * 6.41 * 1.16 } ) = 16° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.16**2-6.41**2-5.3**2 }{ 2 * 5.3 * 6.41 } ) = 3° 28'23" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.03 }{ 6.44 } = 0.16 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.41 }{ 2 * sin 160° 31'37" } = 9.61 ; ;




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

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