# Triangle calculator ASA

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### Right isosceles triangle.

Sides: a = 2.12113203436   b = 1.5   c = 1.5

Area: T = 1.125
Perimeter: p = 5.12113203436
Semiperimeter: s = 2.56106601718

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

Height: ha = 1.06106601718
Height: hb = 1.5
Height: hc = 1.5

Median: ma = 1.06106601718
Median: mb = 1.67770509831
Median: mc = 1.67770509831

Vertex coordinates: A[1.5; 0] B[0; 0] C[1.5; 1.5]
Centroid: CG[1; 0.5]
Coordinates of the circumscribed circle: U[0.75; 0.75]
Coordinates of the inscribed circle: I[1.06106601718; 0.43993398282]

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    