# Triangle calculator ASA

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

### Right isosceles triangle.

Sides: a = 40   b = 56.56985424949   c = 40

Area: T = 800
Perimeter: p = 136.5698542495
Semiperimeter: s = 68.28442712475

Angle ∠ A = α = 45° = 0.78553981634 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 40
Height: hb = 28.28442712475
Height: hc = 40

Median: ma = 44.721135955
Median: mb = 28.28442712475
Median: mc = 44.721135955

Inradius: r = 11.71657287525
Circumradius: R = 28.28442712475

Vertex coordinates: A[40; 0] B[0; 0] C[-0; 40]
Centroid: CG[13.33333333333; 13.33333333333]
Coordinates of the circumscribed circle: U[20; 20]
Coordinates of the inscribed circle: I[11.71657287525; 11.71657287525]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135° = 0.78553981634 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 135° = 0.78553981634 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    