# Triangle calculator ASA

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

### Acute scalene triangle.

Sides: a = 99.42988579437   b = 105.7098868259   c = 50

Area: T = 2467.193325785
Perimeter: p = 255.1387726203
Semiperimeter: s = 127.5698863102

Angle ∠ A = α = 69° = 1.20442771839 rad
Angle ∠ B = β = 83° = 1.44986232792 rad
Angle ∠ C = γ = 28° = 0.48986921906 rad

Height: ha = 49.62773075821
Height: hb = 46.67990213249
Height: hc = 98.68877303141

Median: ma = 66.07331259011
Median: mb = 58.30548684831
Median: mc = 99.52550285624

Inradius: r = 19.34400897199
Circumradius: R = 53.25113617047

Vertex coordinates: A[50; 0] B[0; 0] C[12.11773296331; 98.68877303141]
Centroid: CG[20.70657765444; 32.89659101047]
Coordinates of the circumscribed circle: U[25; 47.01881616337]
Coordinates of the inscribed circle: I[21.86599948422; 19.34400897199]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 111° = 1.20442771839 rad
∠ B' = β' = 97° = 1.44986232792 rad
∠ C' = γ' = 152° = 0.48986921906 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    