# Triangle calculator ASA

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### Right isosceles triangle.

Sides: a = 38.89108729653   b = 38.89108729653   c = 55

Area: T = 756.25
Perimeter: p = 132.782174593
Semiperimeter: s = 66.39108729653

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

Height: ha = 38.89108729653
Height: hb = 38.89108729653
Height: hc = 27.5

Median: ma = 43.48113178273
Median: mb = 43.48113178273
Median: mc = 27.5

Vertex coordinates: A[55; 0] B[0; 0] C[27.5; 27.5]
Centroid: CG[27.5; 9.16766666667]
Coordinates of the circumscribed circle: U[27.5; -0]
Coordinates of the inscribed circle: I[27.5; 11.39108729653]

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