# Triangle calculator ASA

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

### Obtuse scalene triangle.

Sides: a = 29.87992351578   b = 413.7411167802   c = 405

Area: T = 5844.3787794
Perimeter: p = 848.622040296
Semiperimeter: s = 424.311020148

Angle ∠ A = α = 4° = 0.07698131701 rad
Angle ∠ B = β = 105° = 1.83325957146 rad
Angle ∠ C = γ = 71° = 1.23991837689 rad

Height: ha = 391.2199959647
Height: hb = 28.25113718664
Height: hc = 28.86111249087

Median: ma = 409.1211234836
Median: mb = 199.157683735
Median: mc = 212.2055116135

Inradius: r = 13.77438328553
Circumradius: R = 214.168818794

Vertex coordinates: A[405; 0] B[0; 0] C[-7.73333151119; 28.86111249087]
Centroid: CG[132.4222228296; 9.62203749696]
Coordinates of the circumscribed circle: U[202.5; 69.72663416912]
Coordinates of the inscribed circle: I[10.56990336778; 13.77438328553]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176° = 0.07698131701 rad
∠ B' = β' = 75° = 1.83325957146 rad
∠ C' = γ' = 109° = 1.23991837689 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    