# Triangle calculator ASA

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

### Right scalene triangle.

Sides: a = 71.79774009133   b = 46.15504797148   c = 55

Area: T = 1269.138819216
Perimeter: p = 172.9487880628
Semiperimeter: s = 86.4743940314

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 40° = 0.69881317008 rad
Angle ∠ C = γ = 50° = 0.8732664626 rad

Height: ha = 35.35333185328
Height: hb = 55
Height: hc = 46.15504797148

Median: ma = 35.89987004566
Median: mb = 59.64545026342
Median: mc = 53.72325909455

Inradius: r = 14.67765394007
Circumradius: R = 35.89987004566

Vertex coordinates: A[55; 0] B[0; 0] C[55; 46.15504797148]
Centroid: CG[36.66766666667; 15.38334932383]
Coordinates of the circumscribed circle: U[27.5; 23.07552398574]
Coordinates of the inscribed circle: I[40.32334605993; 14.67765394007]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 140° = 0.69881317008 rad
∠ C' = γ' = 130° = 0.8732664626 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    