# Triangle calculator

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

### Right scalene triangle.

Sides: a = 600.6321864937   b = 1415   c = 1537.219993403

Area: T = 424947.0444443
Perimeter: p = 3552.832179897
Semiperimeter: s = 1776.416589948

Angle ∠ A = α = 23° = 0.4011425728 rad
Angle ∠ B = β = 67° = 1.16993705988 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 1415
Height: hb = 600.6321864937
Height: hc = 552.8854546812

Median: ma = 1446.518811578
Median: mb = 928.0710518429
Median: mc = 768.6599967014

Inradius: r = 239.2165965454
Circumradius: R = 768.6599967014

Vertex coordinates: A[1537.219993403; 0] B[0; 0] C[234.6865566393; 552.8854546812]
Centroid: CG[590.6298500141; 184.2954848937]
Coordinates of the circumscribed circle: U[768.6599967014; 0]
Coordinates of the inscribed circle: I[361.4165899482; 239.2165965454]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157° = 0.4011425728 rad
∠ B' = β' = 113° = 1.16993705988 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: side b, angle α and angle γ. ### 2. From angle α and angle γ we calculate angle β: ### 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: ### 4. Calculation of the third side c of the triangle using a 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. ### 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    