# Triangle calculator

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

### Obtuse scalene triangle.

Sides: a = 46   b = 63.99881197287   c = 37

Area: T = 837.1989832202
Perimeter: p = 146.9988119729
Semiperimeter: s = 73.49990598643

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 100.3366211802° = 100°20'10″ = 1.75111972549 rad
Angle ∠ C = γ = 34.66437881979° = 34°39'50″ = 0.60549972353 rad

Height: ha = 36.43995579218
Height: hb = 26.16329509039
Height: hc = 45.25435044433

Median: ma = 46.9440171116
Median: mb = 26.80659726143
Median: mc = 52.57702355369

Inradius: r = 11.39904835483
Circumradius: R = 32.52769119346

Vertex coordinates: A[37; 0] B[0; 0] C[-8.25435044433; 45.25435044433]
Centroid: CG[9.58221651856; 15.08545014811]
Coordinates of the circumscribed circle: U[18.5; 26.75435044433]
Coordinates of the inscribed circle: I[9.50109401357; 11.39904835483]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 79.66437881979° = 79°39'50″ = 1.75111972549 rad
∠ C' = γ' = 145.3366211802° = 145°20'10″ = 0.60549972353 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, c and angle α. ### 2. From angle α, side c and side a we calculate side b - 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    