# Triangle calculator

You have entered side a, angle α and angle β.

### Acute scalene triangle.

Sides: a = 42   b = 30.0366200402   c = 34.19899583527

Area: T = 507.6954979393
Perimeter: p = 106.2266158755
Semiperimeter: s = 53.11330793773

Angle ∠ A = α = 81.4° = 81°24' = 1.42106980111 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 53.6° = 53°36' = 0.93554964791 rad

Height: ha = 24.17659513997
Height: hb = 33.80655394889
Height: hc = 29.69884848098

Median: ma = 24.3843668579
Median: mb = 35.22768830928
Median: mc = 32.26221814863

Vertex coordinates: A[34.19899583527; 0] B[0; 0] C[29.69884848098; 29.69884848098]
Centroid: CG[21.29661477208; 9.89994949366]
Coordinates of the circumscribed circle: U[17.09549791763; 12.60435056335]
Coordinates of the inscribed circle: I[23.07768789754; 9.55987562488]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.6° = 98°36' = 1.42106980111 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 126.4° = 126°24' = 0.93554964791 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, angle α and angle β. ### 2. From angle α and angle β we calculate angle γ: ### 3. From angle β, angle α and side a we calculate side b - By using the law of sines, we calculate unknown side b: ### 4. From angle γ, angle α and side a we calculate side c - By using the law of sines, we calculate unknown side c: 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. ### 5. The triangle circumference is the sum of the lengths of its three sides ### 6. Semiperimeter of the triangle ### 7. The triangle area using Heron's formula ### 8. Calculate the heights of the triangle from its area. ### 9. Calculation of the inner angles of the triangle using a Law of Cosines    