Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=14.48106911099 and with side c=5.24656059882

#1 Acute scalene triangle.

Sides: a = 12.35   b = 8.75   c = 14.48106911099

Area: T = 53.81332567882
Perimeter: p = 35.58106911099
Semiperimeter: s = 17.7990345555

Angle ∠ A = α = 58.14985238878° = 58°8'55″ = 1.0154883197 rad
Angle ∠ B = β = 37° = 0.64657718232 rad
Angle ∠ C = γ = 84.85114761122° = 84°51'5″ = 1.48109376333 rad

Height: ha = 8.71546974556
Height: hb = 12.33001729802
Height: hc = 7.43224155359

Median: ma = 10.24767474113
Median: mb = 12.72765797648
Median: mc = 7.8821617616

Inradius: r = 3.02548573094
Circumradius: R = 7.27696756174

Vertex coordinates: A[14.48106911099; 0] B[0; 0] C[9.86331485491; 7.43224155359]
Centroid: CG[8.11546132197; 2.47774718453]
Coordinates of the circumscribed circle: U[7.2440345555; 0.6522364796]
Coordinates of the inscribed circle: I[9.0440345555; 3.02548573094]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.8511476112° = 121°51'5″ = 1.0154883197 rad
∠ B' = β' = 143° = 0.64657718232 rad
∠ C' = γ' = 95.14985238878° = 95°8'55″ = 1.48109376333 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 = 12.35 ; ; b = 8.75 ; ; c = 14.48 ; ;

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

p = a+b+c = 12.35+8.75+14.48 = 35.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35.58 }{ 2 } = 17.79 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.79 * (17.79-12.35)(17.79-8.75)(17.79-14.48) } ; ; T = sqrt{ 2895.87 } = 53.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.81 }{ 12.35 } = 8.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.81 }{ 8.75 } = 12.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.81 }{ 14.48 } = 7.43 ; ;

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{ 12.35**2-8.75**2-14.48**2 }{ 2 * 8.75 * 14.48 } ) = 58° 8'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.75**2-12.35**2-14.48**2 }{ 2 * 12.35 * 14.48 } ) = 37° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.48**2-12.35**2-8.75**2 }{ 2 * 8.75 * 12.35 } ) = 84° 51'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.81 }{ 17.79 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.35 }{ 2 * sin 58° 8'55" } = 7.27 ; ;





#2 Obtuse scalene triangle.

Sides: a = 12.35   b = 8.75   c = 5.24656059882

Area: T = 19.49437617211
Perimeter: p = 26.34656059882
Semiperimeter: s = 13.17328029941

Angle ∠ A = α = 121.8511476112° = 121°51'5″ = 2.12767094566 rad
Angle ∠ B = β = 37° = 0.64657718232 rad
Angle ∠ C = γ = 21.14985238878° = 21°8'55″ = 0.36991113738 rad

Height: ha = 3.15768844893
Height: hb = 4.45657169648
Height: hc = 7.43224155359

Median: ma = 3.72994525191
Median: mb = 8.41989557602
Median: mc = 10.37660977469

Inradius: r = 1.48798491809
Circumradius: R = 7.27696756174

Vertex coordinates: A[5.24656059882; 0] B[0; 0] C[9.86331485491; 7.43224155359]
Centroid: CG[5.03662515124; 2.47774718453]
Coordinates of the circumscribed circle: U[2.62328029941; 6.788005074]
Coordinates of the inscribed circle: I[4.42328029941; 1.48798491809]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 58.14985238878° = 58°8'55″ = 2.12767094566 rad
∠ B' = β' = 143° = 0.64657718232 rad
∠ C' = γ' = 158.8511476112° = 158°51'5″ = 0.36991113738 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 12.35 ; ; b = 8.75 ; ; beta = 37° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 8.75**2 = 12.35**2 + c**2 -2 * 8.75 * c * cos (37° ) ; ; ; ; c**2 -19.726c +75.96 =0 ; ; p=1; q=-19.7262970982; r=75.96 ; ; D = q**2 - 4pr = 19.726**2 - 4 * 1 * 75.96 = 85.2867972052 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 19.73 ± sqrt{ 85.29 } }{ 2 } ; ; c_{1,2} = 9.86314854908 ± 4.61754256085 ; ;
c_{1} = 14.4806911099 ; ; c_{2} = 5.24560598823 ; ; ; ; (c -14.4806911099) (c -5.24560598823) = 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 = 12.35 ; ; b = 8.75 ; ; c = 5.25 ; ;

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

p = a+b+c = 12.35+8.75+5.25 = 26.35 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.35 }{ 2 } = 13.17 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.17 * (13.17-12.35)(13.17-8.75)(13.17-5.25) } ; ; T = sqrt{ 380.01 } = 19.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.49 }{ 12.35 } = 3.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.49 }{ 8.75 } = 4.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.49 }{ 5.25 } = 7.43 ; ;

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{ 12.35**2-8.75**2-5.25**2 }{ 2 * 8.75 * 5.25 } ) = 121° 51'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.75**2-12.35**2-5.25**2 }{ 2 * 12.35 * 5.25 } ) = 37° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.25**2-12.35**2-8.75**2 }{ 2 * 8.75 * 12.35 } ) = 21° 8'55" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.49 }{ 13.17 } = 1.48 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.35 }{ 2 * sin 121° 51'5" } = 7.27 ; ;




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

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