# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 16.7755349753   b = 32.36106439249   c = 37.5

Area: T = 270.7365910315
Perimeter: p = 86.6365993678
Semiperimeter: s = 43.3187996839

Angle ∠ A = α = 26.5° = 26°30' = 0.46325122518 rad
Angle ∠ B = β = 59.4° = 59°24' = 1.03767255757 rad
Angle ∠ C = γ = 94.1° = 94°6' = 1.64223548261 rad

Height: ha = 32.27878260126
Height: hb = 16.73224179916
Height: hc = 14.43992485501

Median: ma = 34.006555172
Median: mb = 24.12552639542
Median: mc = 17.68547198815

Inradius: r = 6.25499637581
Circumradius: R = 18.798810844

Vertex coordinates: A[37.5; 0] B[0; 0] C[8.5399347788; 14.43992485501]
Centroid: CG[15.34664492627; 4.813308285]
Coordinates of the circumscribed circle: U[18.75; -1.34440167117]
Coordinates of the inscribed circle: I[10.9577352914; 6.25499637581]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.5° = 153°30' = 0.46325122518 rad
∠ B' = β' = 120.6° = 120°36' = 1.03767255757 rad
∠ C' = γ' = 85.9° = 85°54' = 1.64223548261 rad

# How did we calculate this triangle?

### 1. Input data entered: side c, angle α 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    