# Triangle calculator

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

### Acute scalene triangle.

Sides: a = 13.6   b = 13.417703685   c = 6.76768446247

Area: T = 44.23220180725
Perimeter: p = 33.78438814747
Semiperimeter: s = 16.89219407373

Angle ∠ A = α = 77° = 1.3443903524 rad
Angle ∠ B = β = 74° = 1.29215436465 rad
Angle ∠ C = γ = 29° = 0.50661454831 rad

Height: ha = 6.50547085401
Height: hb = 6.59334108354
Height: hc = 13.07331590648

Median: ma = 8.16547738489
Median: mb = 8.38987349242
Median: mc = 13.07882602961

Inradius: r = 2.6198527898
Circumradius: R = 6.9798867933

Vertex coordinates: A[6.76768446247; 0] B[0; 0] C[3.74986680391; 13.07331590648]
Centroid: CG[3.50551708879; 4.35877196883]
Coordinates of the circumscribed circle: U[3.38334223123; 6.10438554277]
Coordinates of the inscribed circle: I[3.47549038873; 2.6198527898]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103° = 1.3443903524 rad
∠ B' = β' = 106° = 1.29215436465 rad
∠ C' = γ' = 151° = 0.50661454831 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    