# Triangle calculator

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

### Right scalene triangle.

Sides: a = 184.3310521802   b = 3005.65876221   c = 3000

Area: T = 276495.7832703
Perimeter: p = 6189.98881439
Semiperimeter: s = 3094.994407195

Angle ∠ A = α = 3.51660333917° = 3°30'58″ = 0.06113663593 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 86.48439666083° = 86°29'2″ = 1.50994299675 rad

Height: ha = 3000
Height: hb = 183.9843551999
Height: hc = 184.3310521802

Median: ma = 3001.415540532
Median: mb = 1502.829881105
Median: mc = 1511.283347482

Inradius: r = 89.33664498526
Circumradius: R = 1502.829881105

Vertex coordinates: A[3000; 0] B[0; 0] C[-0; 184.3310521802]
Centroid: CG[1000; 61.44435072673]
Coordinates of the circumscribed circle: U[1500; 92.1655260901]
Coordinates of the inscribed circle: I[89.33664498526; 89.33664498526]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.4843966608° = 176°29'2″ = 0.06113663593 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 93.51660333917° = 93°30'58″ = 1.50994299675 rad

# How did we calculate this triangle?

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