# Triangle calculator

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

### Acute isosceles triangle.

Sides: a = 50   b = 21.64439613938   c = 50

Area: T = 528.2732827176
Perimeter: p = 121.6443961394
Semiperimeter: s = 60.82219806969

Angle ∠ A = α = 77.5° = 77°30' = 1.35326301703 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 77.5° = 77°30' = 1.35326301703 rad

Height: ha = 21.1310913087
Height: hb = 48.8154800356
Height: hc = 21.1310913087

Median: ma = 29.31326343478
Median: mb = 48.8154800356
Median: mc = 29.31326343478

Inradius: r = 8.68655577724
Circumradius: R = 25.60769878579

Vertex coordinates: A[50; 0] B[0; 0] C[45.31553893518; 21.1310913087]
Centroid: CG[31.77217964506; 7.04436376957]
Coordinates of the circumscribed circle: U[25; 5.54223665661]
Coordinates of the inscribed circle: I[39.17880193031; 8.68655577724]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 102.5° = 102°30' = 1.35326301703 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 102.5° = 102°30' = 1.35326301703 rad

# How did we calculate this triangle?

### 1. Input data entered: side a, c and angle β. ### 2. 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. ### 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    