Triangle calculator - result

You have entered side b, angle α and angle β.

Acute scalene triangle.

Sides: a = 14.97325484853   b = 13   c = 11.51992819451

Area: T = 72.32440175519
Perimeter: p = 39.49218304304
Semiperimeter: s = 19.74659152152

Angle ∠ A = α = 75° = 1.3098996939 rad
Angle ∠ B = β = 57° = 0.99548376736 rad
Angle ∠ C = γ = 48° = 0.8387758041 rad

Height: ha = 9.66108827312
Height: hb = 11.12767719311
Height: hc = 12.55770357418

Median: ma = 9.73766640195
Median: mb = 11.67698557119
Median: mc = 12.78333931309

Vertex coordinates: A[11.51992819451; 0] B[0; 0] C[8.15546343588; 12.55770357418]
Centroid: CG[6.55879721013; 4.18656785806]
Coordinates of the circumscribed circle: U[5.76596409725; 5.18660040254]
Coordinates of the inscribed circle: I[6.74659152152; 3.66327331154]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105° = 1.3098996939 rad
∠ B' = β' = 123° = 0.99548376736 rad
∠ C' = γ' = 132° = 0.8387758041 rad

How did we calculate this triangle?

1. Input data entered: side b, angle α and angle β. 2. From angle α and angle β we calculate angle γ: 3. From angle α, angle β and side b we calculate side a - By using the law of sines, we calculate unknown side a: 4. Calculation of the third side c of the triangle using a Law of Cosines 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. 5. The triangle circumference is the sum of the lengths of its three sides 6. Semiperimeter of the triangle 7. The triangle area using Heron's formula 8. Calculate the heights of the triangle from its area. 9. Calculation of the inner angles of the triangle using a Law of Cosines    