Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=8605.469875945 and with side c=1373.65334674

#1 Acute scalene triangle.

Sides: a = 7986   b = 7208   c = 8605.469875945

Area: T = 26829360.60114
Perimeter: p = 23799.46987595
Semiperimeter: s = 11899.73443797

Angle ∠ A = α = 59.89106439657° = 59°53'26″ = 1.04552889283 rad
Angle ∠ B = β = 51.3333333° = 51°20' = 0.89659356769 rad
Angle ∠ C = γ = 68.77660230343° = 68°46'34″ = 1.22003680484 rad

Height: ha = 6719.099857285
Height: hb = 7444.329869073
Height: hc = 6235.421106801

Median: ma = 6860.075502036
Median: mb = 7478.391075503
Median: mc = 6273.134373503

Inradius: r = 2254.618844317
Circumradius: R = 4615.814402219

Vertex coordinates: A[8605.469875945; 0] B[0; 0] C[4989.561111342; 6235.421106801]
Centroid: CG[4531.677662429; 2078.474368934]
Coordinates of the circumscribed circle: U[4302.734437973; 1670.993250297]
Coordinates of the inscribed circle: I[4691.734437973; 2254.618844317]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120.1099356034° = 120°6'34″ = 1.04552889283 rad
∠ B' = β' = 128.6676667° = 128°40' = 0.89659356769 rad
∠ C' = γ' = 111.2243976966° = 111°13'26″ = 1.22003680484 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 = 7986 ; ; b = 7208 ; ; c = 8605.47 ; ;

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

p = a+b+c = 7986+7208+8605.47 = 23799.47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23799.47 }{ 2 } = 11899.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11899.73 * (11899.73-7986)(11899.73-7208)(11899.73-8605.47) } ; ; T = sqrt{ 7.198 * 10**{ 14 } } = 26829360.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26829360.6 }{ 7986 } = 6719.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26829360.6 }{ 7208 } = 7444.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26829360.6 }{ 8605.47 } = 6235.42 ; ;

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{ 7986**2-7208**2-8605.47**2 }{ 2 * 7208 * 8605.47 } ) = 59° 53'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7208**2-7986**2-8605.47**2 }{ 2 * 7986 * 8605.47 } ) = 51° 20' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8605.47**2-7986**2-7208**2 }{ 2 * 7208 * 7986 } ) = 68° 46'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26829360.6 }{ 11899.73 } = 2254.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7986 }{ 2 * sin 59° 53'26" } = 4615.81 ; ;





#2 Obtuse scalene triangle.

Sides: a = 7986   b = 7208   c = 1373.65334674

Area: T = 4282653.885538
Perimeter: p = 16567.65334674
Semiperimeter: s = 8283.82767337

Angle ∠ A = α = 120.1099356034° = 120°6'34″ = 2.09663037252 rad
Angle ∠ B = β = 51.3333333° = 51°20' = 0.89659356769 rad
Angle ∠ C = γ = 8.55773109657° = 8°33'26″ = 0.14993532515 rad

Height: ha = 1072.544041707
Height: hb = 1188.306573956
Height: hc = 6235.421106801

Median: ma = 3313.162237517
Median: mb = 4454.51994942
Median: mc = 7575.883272335

Inradius: r = 516.9989795061
Circumradius: R = 4615.814402219

Vertex coordinates: A[1373.65334674; 0] B[0; 0] C[4989.561111342; 6235.421106801]
Centroid: CG[2121.072152694; 2078.474368934]
Coordinates of the circumscribed circle: U[686.8276733699; 4564.429856504]
Coordinates of the inscribed circle: I[1075.82767337; 516.9989795061]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 59.89106439657° = 59°53'26″ = 2.09663037252 rad
∠ B' = β' = 128.6676667° = 128°40' = 0.89659356769 rad
∠ C' = γ' = 171.4432689034° = 171°26'34″ = 0.14993532515 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 7986 ; ; b = 7208 ; ; beta = 51° 20' ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 7208**2 = 7986**2 + c**2 -2 * 7208 * c * cos (51° 20') ; ; ; ; c**2 -9979.122c +11820932 =0 ; ; p=1; q=-9979.12222685; r=11820932 ; ; D = q**2 - 4pr = 9979.122**2 - 4 * 1 * 11820932 = 52299152.4184 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 9979.12 ± sqrt{ 52299152.42 } }{ 2 } ; ; c_{1,2} = 4989.56111342 ± 3615.90764603 ; ;
c_{1} = 8605.46875945 ; ; c_{2} = 1373.6534674 ; ; ; ; (c -8605.46875945) (c -1373.6534674) = 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 = 7986 ; ; b = 7208 ; ; c = 1373.65 ; ;

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

p = a+b+c = 7986+7208+1373.65 = 16567.65 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16567.65 }{ 2 } = 8283.83 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8283.83 * (8283.83-7986)(8283.83-7208)(8283.83-1373.65) } ; ; T = sqrt{ 1.834 * 10**{ 13 } } = 4282653.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4282653.89 }{ 7986 } = 1072.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4282653.89 }{ 7208 } = 1188.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4282653.89 }{ 1373.65 } = 6235.42 ; ;

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{ 7986**2-7208**2-1373.65**2 }{ 2 * 7208 * 1373.65 } ) = 120° 6'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7208**2-7986**2-1373.65**2 }{ 2 * 7986 * 1373.65 } ) = 51° 20' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1373.65**2-7986**2-7208**2 }{ 2 * 7208 * 7986 } ) = 8° 33'26" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4282653.89 }{ 8283.83 } = 516.99 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7986 }{ 2 * sin 120° 6'34" } = 4615.81 ; ;




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

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