# Triangle calculator ASA

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### Right isosceles triangle.

Sides: a = 424.2644068712   b = 300   c = 300

Area: T = 45000
Perimeter: p = 1024.264406871
Semiperimeter: s = 512.1322034356

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

Height: ha = 212.1322034356
Height: hb = 300
Height: hc = 300

Median: ma = 212.1322034356
Median: mb = 335.4110196625
Median: mc = 335.4110196625

Vertex coordinates: A[300; 0] B[0; 0] C[300; 300]
Centroid: CG[200; 100]
Coordinates of the circumscribed circle: U[150; 150]
Coordinates of the inscribed circle: I[212.1322034356; 87.8687965644]

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