# Triangle calculator ASA

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### Acute isosceles triangle.

Sides: a = 109.9099240141   b = 102   c = 102

Area: T = 4722.258844333
Perimeter: p = 313.9099240141
Semiperimeter: s = 156.9554620071

Angle ∠ A = α = 65.2° = 65°12' = 1.13879546723 rad
Angle ∠ B = β = 57.4° = 57°24' = 1.00218189906 rad
Angle ∠ C = γ = 57.4° = 57°24' = 1.00218189906 rad

Height: ha = 85.93301444947
Height: hb = 92.59333028104
Height: hc = 92.59333028104

Median: ma = 85.93301444947
Median: mb = 92.9577089747
Median: mc = 92.9577089747

Vertex coordinates: A[102; 0] B[0; 0] C[59.21658875905; 92.59333028104]
Centroid: CG[53.73986291968; 30.86444342701]
Coordinates of the circumscribed circle: U[51; 32.61658607097]
Coordinates of the inscribed circle: I[54.95546200707; 30.08767756629]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.8° = 114°48' = 1.13879546723 rad
∠ B' = β' = 122.6° = 122°36' = 1.00218189906 rad
∠ C' = γ' = 122.6° = 122°36' = 1.00218189906 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    