# Triangle calculator ASA

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

### Acute isosceles triangle.

Sides: a = 5.42220864676   b = 5.42220864676   c = 6.97105

Area: T = 14.47661922317
Perimeter: p = 17.81546729351
Semiperimeter: s = 8.90773364676

Angle ∠ A = α = 50° = 0.8732664626 rad
Angle ∠ B = β = 50° = 0.8732664626 rad
Angle ∠ C = γ = 80° = 1.39662634016 rad

Height: ha = 5.34397127908
Height: hb = 5.34397127908
Height: hc = 4.15435592086

Median: ma = 5.62552724859
Median: mb = 5.62552724859
Median: mc = 4.15435592086

Inradius: r = 1.62551987656
Circumradius: R = 3.53990155991

Vertex coordinates: A[6.97105; 0] B[0; 0] C[3.485525; 4.15435592086]
Centroid: CG[3.485525; 1.38545197362]
Coordinates of the circumscribed circle: U[3.485525; 0.61545436095]
Coordinates of the inscribed circle: I[3.485525; 1.62551987656]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130° = 0.8732664626 rad
∠ B' = β' = 130° = 0.8732664626 rad
∠ C' = γ' = 100° = 1.39662634016 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    