# Triangle calculator SSA

Please enter two sides and a non-included angle
°

Triangle has two solutions with side c=114.8532813742 and with side c=54.85328137424

### #1 Acute scalene triangle.

Sides: a = 120   b = 90   c = 114.8532813742

Area: T = 4872.792220614
Perimeter: p = 324.8532813742
Semiperimeter: s = 162.4266406871

Angle ∠ A = α = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 64.47112206345° = 64°28'16″ = 1.12552350729 rad

Height: ha = 81.21332034356
Height: hb = 108.2844271248
Height: hc = 84.85328137424

Median: ma = 83.9387979558
Median: mb = 108.4922324209
Median: mc = 89.17551523344

Inradius: r = 30
Circumradius: R = 63.64396103068

Vertex coordinates: A[114.8532813742; 0] B[0; 0] C[84.85328137424; 84.85328137424]
Centroid: CG[66.56985424949; 28.28442712475]
Coordinates of the circumscribed circle: U[57.42664068712; 27.42664068712]
Coordinates of the inscribed circle: I[72.42664068712; 30]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 115.5298779366° = 115°31'44″ = 1.12552350729 rad

# How did we calculate this triangle?

### 1. Use Law of Cosines  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. ### 2. The triangle circumference is the sum of the lengths of its three sides ### 3. Semiperimeter of the triangle ### 4. The triangle area using Heron's formula ### 5. Calculate the heights of the triangle from its area. ### 6. Calculation of the inner angles of the triangle using a Law of Cosines   ### 9. Calculation of medians ### #2 Obtuse scalene triangle.

Sides: a = 120   b = 90   c = 54.85328137424

Area: T = 2327.208779386
Perimeter: p = 264.8532813742
Semiperimeter: s = 132.4266406871

Angle ∠ A = α = 109.4711220634° = 109°28'16″ = 1.91106332362 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 25.52987793655° = 25°31'44″ = 0.44655612539 rad

Height: ha = 38.78767965644
Height: hb = 51.71657287525
Height: hc = 84.85328137424

Median: ma = 44.20987727462
Median: mb = 81.72876916824
Median: mc = 102.4598734162

Inradius: r = 17.57435931288
Circumradius: R = 63.64396103068

Vertex coordinates: A[54.85328137424; 0] B[0; 0] C[84.85328137424; 84.85328137424]
Centroid: CG[46.56985424949; 28.28442712475]
Coordinates of the circumscribed circle: U[27.42664068712; 57.42664068712]
Coordinates of the inscribed circle: I[42.42664068712; 17.57435931288]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 70.52987793655° = 70°31'44″ = 1.91106332362 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 154.4711220634° = 154°28'16″ = 0.44655612539 rad

# How did we calculate this triangle?

### 1. Use Law of Cosines  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. ### 2. The triangle circumference is the sum of the lengths of its three sides ### 3. Semiperimeter of the triangle ### 4. The triangle area using Heron's formula ### 5. Calculate the heights of the triangle from its area. ### 6. Calculation of the inner angles of the triangle using a Law of Cosines    