# Triangle calculator

You have entered side a, b and angle β.

### Right scalene triangle.

Sides: a = 307.715   b = 347   c = 160.3766054244

Area: T = 24675.05987659
Perimeter: p = 815.0911054244
Semiperimeter: s = 407.5465527122

Angle ∠ A = α = 62.47222069266° = 62°28'20″ = 1.09903457019 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 27.52877930734° = 27°31'40″ = 0.48804506249 rad

Height: ha = 160.3766054244
Height: hb = 142.2199358881
Height: hc = 307.715

Median: ma = 222.2444480429
Median: mb = 173.5
Median: mc = 317.992157366

Vertex coordinates: A[160.3766054244; 0] B[0; 0] C[-0; 307.715]
Centroid: CG[53.45986847481; 102.5721666667]
Coordinates of the circumscribed circle: U[80.18880271222; 153.85875]
Coordinates of the inscribed circle: I[60.54655271222; 60.54655271222]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.5287793073° = 117°31'40″ = 1.09903457019 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 152.4722206927° = 152°28'20″ = 0.48804506249 rad

# How did we calculate this triangle?

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