# Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles
°
°

### Acute isosceles triangle.

Sides: a = 166.1644014112   b = 166.1644014112   c = 200

Area: T = 13270.44882162
Perimeter: p = 532.3288028225
Semiperimeter: s = 266.1644014112

Angle ∠ A = α = 53° = 0.92550245036 rad
Angle ∠ B = β = 53° = 0.92550245036 rad
Angle ∠ C = γ = 74° = 1.29215436465 rad

Height: ha = 159.7277102009
Height: hb = 159.7277102009
Height: hc = 132.7044482162

Median: ma = 164.0220181369
Median: mb = 164.0220181369
Median: mc = 132.7044482162

Inradius: r = 49.85881608053
Circumradius: R = 104.0329943586

Vertex coordinates: A[200; 0] B[0; 0] C[100; 132.7044482162]
Centroid: CG[100; 44.23548273873]
Coordinates of the circumscribed circle: U[100; 28.67545385759]
Coordinates of the inscribed circle: I[100; 49.85881608053]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127° = 0.92550245036 rad
∠ B' = β' = 127° = 0.92550245036 rad
∠ C' = γ' = 106° = 1.29215436465 rad

# How did we calculate this triangle?

### 1. Calculate the third unknown inner angle ### 2. By using the law of sines, we calculate unknown side a ### 3. By using the law of sines, we calculate last unknown side b 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. ### 4. The triangle circumference is the sum of the lengths of its three sides ### 5. Semiperimeter of the triangle ### 6. The triangle area using Heron's formula ### 7. Calculate the heights of the triangle from its area. ### 8. Calculation of the inner angles of the triangle using a Law of Cosines    