# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 1.27   b = 3.78   c = 4.5366427824

Area: T = 2.09661349022
Perimeter: p = 9.5866427824
Semiperimeter: s = 4.7933213912

Angle ∠ A = α = 14.15111081903° = 14°9'4″ = 0.24769834307 rad
Angle ∠ B = β = 46.691° = 46°41'28″ = 0.8154911681 rad
Angle ∠ C = γ = 119.158789181° = 119°9'28″ = 2.08796975418 rad

Height: ha = 3.30109998459
Height: hb = 1.10990660858
Height: hc = 0.92441345761

Median: ma = 4.12768103544
Median: mb = 2.74329798944
Median: mc = 1.67550688492

Inradius: r = 0.43773130306
Circumradius: R = 2.59773489814

Vertex coordinates: A[4.5366427824; 0] B[0; 0] C[0.87111344817; 0.92441345761]
Centroid: CG[1.80325207686; 0.30880448587]
Coordinates of the circumscribed circle: U[2.2688213912; -1.265547516]
Coordinates of the inscribed circle: I[1.0133213912; 0.43773130306]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.849889181° = 165°50'56″ = 0.24769834307 rad
∠ B' = β' = 133.309° = 133°18'32″ = 0.8154911681 rad
∠ C' = γ' = 60.84221081903° = 60°50'32″ = 2.08796975418 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    