# Triangle calculator

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

### Acute scalene triangle.

Sides: a = 19.2   b = 20.76994277294   c = 21.63334471857

Area: T = 181.2899411096
Perimeter: p = 61.60328749151
Semiperimeter: s = 30.80114374576

Angle ∠ A = α = 53.8° = 53°48' = 0.93989871376 rad
Angle ∠ B = β = 60.8° = 60°48' = 1.06111601852 rad
Angle ∠ C = γ = 65.4° = 65°24' = 1.14114453308 rad

Height: ha = 18.88443136558
Height: hb = 17.45773332937
Height: hc = 16.76601038836

Median: ma = 18.90883997914
Median: mb = 17.62204635727
Median: mc = 16.82326946361

Inradius: r = 5.88657451489
Circumradius: R = 11.89664958444

Vertex coordinates: A[21.63334471857; 0] B[0; 0] C[9.36769054555; 16.76601038836]
Centroid: CG[10.33334508804; 5.58767012945]
Coordinates of the circumscribed circle: U[10.81767235928; 4.95222827152]
Coordinates of the inscribed circle: I[10.03220097281; 5.88657451489]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.2° = 126°12' = 0.93989871376 rad
∠ B' = β' = 119.2° = 119°12' = 1.06111601852 rad
∠ C' = γ' = 114.6° = 114°36' = 1.14114453308 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, angle α and angle γ. ### 2. From angle α and angle γ we calculate angle β: ### 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 ### 10. Inradius ### 11. Circumradius ### 12. Calculation of medians #### Look also our friend's collection of math examples and problems:

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