# Triangle calculator

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

### Right scalene triangle.

Sides: a = 29.625   b = 57   c = 48.69766053745

Area: T = 721.318846711
Perimeter: p = 135.3221605374
Semiperimeter: s = 67.66108026873

Angle ∠ A = α = 31.31546010425° = 31°18'53″ = 0.54765428921 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 58.68553989575° = 58°41'7″ = 1.02442534347 rad

Height: ha = 48.69766053745
Height: hb = 25.30994198986
Height: hc = 29.625

Median: ma = 50.98996024665
Median: mb = 28.5
Median: mc = 38.34768443128

Inradius: r = 10.66108026873
Circumradius: R = 28.5

Vertex coordinates: A[48.69766053745; 0] B[0; 0] C[-0; 29.625]
Centroid: CG[16.23222017915; 9.875]
Coordinates of the circumscribed circle: U[24.34883026873; 14.81325]
Coordinates of the inscribed circle: I[10.66108026873; 10.66108026873]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.6855398958° = 148°41'7″ = 0.54765428921 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 121.3154601042° = 121°18'53″ = 1.02442534347 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    