# Triangle calculator ASA

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

### Acute scalene triangle.

Sides: a = 1229.423286341   b = 1102.277038425   c = 900

Area: T = 479120.1444266
Perimeter: p = 3231.693324766
Semiperimeter: s = 1615.847662383

Angle ∠ A = α = 75° = 1.3098996939 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 779.4232863406
Height: hb = 869.333324366
Height: hc = 1064.71114317

Median: ma = 796.6376589502
Median: mb = 925.7387699639
Median: mc = 1077.377657694

Inradius: r = 296.5133380169
Circumradius: R = 636.3966103068

Vertex coordinates: A[900; 0] B[0; 0] C[614.7111431703; 1064.71114317]
Centroid: CG[504.9043810568; 354.9043810568]
Coordinates of the circumscribed circle: U[450; 450]
Coordinates of the inscribed circle: I[513.5766239577; 296.5133380169]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105° = 1.3098996939 rad
∠ B' = β' = 120° = 1.04771975512 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    