# Triangle calculator

Please enter what you know about the triangle:
You have entered side a, b and angle α.

Triangle has two solutions: a=149; b=176; c=27.54658410637 and a=149; b=176; c=318.5659886399.

### #1 Obtuse scalene triangle.

Sides: a = 149   b = 176   c = 27.54658410637

Area: T = 441.745511228
Perimeter: p = 352.5465841064
Semiperimeter: s = 176.2732920532

Angle ∠ A = α = 10.5° = 10°30' = 0.18332595715 rad
Angle ∠ B = β = 167.5699331838° = 167°34'10″ = 2.92546365659 rad
Angle ∠ C = γ = 1.93106681621° = 1°55'50″ = 0.03436965162 rad

Height: ha = 5.92994645944
Height: hb = 5.02198308214
Height: hc = 32.07334524866

Median: ma = 101.5733306926
Median: mb = 61.12219001664
Median: mc = 162.4777095801

Inradius: r = 2.5066029349
Circumradius: R = 408.8121617816

Vertex coordinates: A[27.54658410637; 0] B[0; 0] C[-145.5077022668; 32.07334524866]
Centroid: CG[-39.3220393868; 10.69111508289]
Coordinates of the circumscribed circle: U[13.77329205318; 408.5879546137]
Coordinates of the inscribed circle: I[0.27329205318; 2.5066029349]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5° = 169°30' = 0.18332595715 rad
∠ B' = β' = 12.43106681621° = 12°25'50″ = 2.92546365659 rad
∠ C' = γ' = 178.0699331838° = 178°4'10″ = 0.03436965162 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle α. ### 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic equation:  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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines   ### 10. Calculation of medians ### #2 Obtuse scalene triangle.

Sides: a = 149   b = 176   c = 318.5659886399

Area: T = 5108.658769028
Perimeter: p = 643.5659886399
Semiperimeter: s = 321.7879943199

Angle ∠ A = α = 10.5° = 10°30' = 0.18332595715 rad
Angle ∠ B = β = 12.43106681621° = 12°25'50″ = 0.21769560877 rad
Angle ∠ C = γ = 157.0699331838° = 157°4'10″ = 2.74113769945 rad

Height: ha = 68.57325864467
Height: hb = 58.05329282986
Height: hc = 32.07334524866

Median: ma = 246.3298947976
Median: mb = 232.5876974294
Median: mc = 34.90655825677

Inradius: r = 15.87662464791
Circumradius: R = 408.8121617816

Vertex coordinates: A[318.5659886399; 0] B[0; 0] C[145.5077022668; 32.07334524866]
Centroid: CG[154.6898969689; 10.69111508289]
Coordinates of the circumscribed circle: U[159.2879943199; -376.506609365]
Coordinates of the inscribed circle: I[145.7879943199; 15.87662464791]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5° = 169°30' = 0.18332595715 rad
∠ B' = β' = 167.5699331838° = 167°34'10″ = 0.21769560877 rad
∠ C' = γ' = 22.93106681621° = 22°55'50″ = 2.74113769945 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, b and angle α. ### 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic equation:  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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines    