Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=63.52334994295 and with side c=11.08325128704

#1 Obtuse scalene triangle.

Sides: a = 48   b = 40   c = 63.52334994295

Area: T = 959.4399204043
Perimeter: p = 151.5233499429
Semiperimeter: s = 75.76217497147

Angle ∠ A = α = 49.04114908974° = 49°2'29″ = 0.85659354862 rad
Angle ∠ B = β = 39° = 0.68106784083 rad
Angle ∠ C = γ = 91.95985091026° = 91°57'31″ = 1.60549787591 rad

Height: ha = 39.97766335018
Height: hb = 47.97219602022
Height: hc = 30.20773787704

Median: ma = 47.34657230369
Median: mb = 52.62771554417
Median: mc = 30.71114189685

Inradius: r = 12.66438997602
Circumradius: R = 31.78803145813

Vertex coordinates: A[63.52334994295; 0] B[0; 0] C[37.30330061499; 30.20773787704]
Centroid: CG[33.60988351931; 10.06991262568]
Coordinates of the circumscribed circle: U[31.76217497147; -1.08661169117]
Coordinates of the inscribed circle: I[35.76217497147; 12.66438997602]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.9598509103° = 130°57'31″ = 0.85659354862 rad
∠ B' = β' = 141° = 0.68106784083 rad
∠ C' = γ' = 88.04114908974° = 88°2'29″ = 1.60549787591 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 48 ; ; b = 40 ; ; beta = 39° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 40**2 = 48**2 + c**2 -2 * 48 * c * cos (39° ) ; ; ; ; c**2 -74.606c +704 =0 ; ; p=1; q=-74.606; r=704 ; ; D = q**2 - 4pr = 74.606**2 - 4 * 1 * 704 = 2750.05707129 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 74.61 ± sqrt{ 2750.06 } }{ 2 } ; ; c_{1,2} = 37.30300615 ± 26.2204932795 ; ; c_{1} = 63.5234994295 ; ;
c_{2} = 11.0825128705 ; ; ; ; (c -63.5234994295) (c -11.0825128705) = 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 = 48 ; ; b = 40 ; ; c = 63.52 ; ;

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

p = a+b+c = 48+40+63.52 = 151.52 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 151.52 }{ 2 } = 75.76 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 75.76 * (75.76-48)(75.76-40)(75.76-63.52) } ; ; T = sqrt{ 920523.59 } = 959.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 959.44 }{ 48 } = 39.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 959.44 }{ 40 } = 47.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 959.44 }{ 63.52 } = 30.21 ; ;

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{ 48**2-40**2-63.52**2 }{ 2 * 40 * 63.52 } ) = 49° 2'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-48**2-63.52**2 }{ 2 * 48 * 63.52 } ) = 39° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 63.52**2-48**2-40**2 }{ 2 * 40 * 48 } ) = 91° 57'31" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 959.44 }{ 75.76 } = 12.66 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 48 }{ 2 * sin 49° 2'29" } = 31.78 ; ;





#2 Obtuse scalene triangle.

Sides: a = 48   b = 40   c = 11.08325128704

Area: T = 167.3876832002
Perimeter: p = 99.08325128704
Semiperimeter: s = 49.54112564352

Angle ∠ A = α = 130.9598509103° = 130°57'31″ = 2.28656571673 rad
Angle ∠ B = β = 39° = 0.68106784083 rad
Angle ∠ C = γ = 10.04114908974° = 10°2'29″ = 0.1755257078 rad

Height: ha = 6.97444513334
Height: hb = 8.36993416001
Height: hc = 30.20773787704

Median: ma = 16.89441127545
Median: mb = 28.522036195
Median: mc = 43.83325732432

Inradius: r = 3.3798736109
Circumradius: R = 31.78803145813

Vertex coordinates: A[11.08325128704; 0] B[0; 0] C[37.30330061499; 30.20773787704]
Centroid: CG[16.12985063401; 10.06991262568]
Coordinates of the circumscribed circle: U[5.54112564352; 31.29334956821]
Coordinates of the inscribed circle: I[9.54112564352; 3.3798736109]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 49.04114908974° = 49°2'29″ = 2.28656571673 rad
∠ B' = β' = 141° = 0.68106784083 rad
∠ C' = γ' = 169.9598509103° = 169°57'31″ = 0.1755257078 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 48 ; ; b = 40 ; ; beta = 39° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 40**2 = 48**2 + c**2 -2 * 48 * c * cos (39° ) ; ; ; ; c**2 -74.606c +704 =0 ; ; p=1; q=-74.606; r=704 ; ; D = q**2 - 4pr = 74.606**2 - 4 * 1 * 704 = 2750.05707129 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 74.61 ± sqrt{ 2750.06 } }{ 2 } ; ; c_{1,2} = 37.30300615 ± 26.2204932795 ; ; c_{1} = 63.5234994295 ; ; : Nr. 1
c_{2} = 11.0825128705 ; ; ; ; (c -63.5234994295) (c -11.0825128705) = 0 ; ; ; ; c>0 ; ; : Nr. 1


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 = 48 ; ; b = 40 ; ; c = 11.08 ; ;

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

p = a+b+c = 48+40+11.08 = 99.08 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 99.08 }{ 2 } = 49.54 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 49.54 * (49.54-48)(49.54-40)(49.54-11.08) } ; ; T = sqrt{ 28018.35 } = 167.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 167.39 }{ 48 } = 6.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 167.39 }{ 40 } = 8.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 167.39 }{ 11.08 } = 30.21 ; ;

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{ 48**2-40**2-11.08**2 }{ 2 * 40 * 11.08 } ) = 130° 57'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-48**2-11.08**2 }{ 2 * 48 * 11.08 } ) = 39° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.08**2-48**2-40**2 }{ 2 * 40 * 48 } ) = 10° 2'29" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 167.39 }{ 49.54 } = 3.38 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 48 }{ 2 * sin 130° 57'31" } = 31.78 ; ;




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

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