Triangle calculator SSA

Please enter two sides and a non-included angle
°

Acute scalene triangle.

Sides: a = 85   b = 90   c = 82.45767306549

Area: T = 3176.075502616
Perimeter: p = 257.4576730655
Semiperimeter: s = 128.7288365327

Angle ∠ A = α = 58.86656606444° = 58°51'56″ = 1.02773995946 rad
Angle ∠ B = β = 65° = 1.13444640138 rad
Angle ∠ C = γ = 56.13443393556° = 56°8'4″ = 0.98797290452 rad

Height: ha = 74.73111770861
Height: hb = 70.57994450258
Height: hc = 77.03661618981

Median: ma = 75.12219423015
Median: mb = 70.61990924265
Median: mc = 77.21986628506

Inradius: r = 24.67326897998
Circumradius: R = 49.65220063533

Vertex coordinates: A[82.45767306549; 0] B[0; 0] C[35.9232552248; 77.03661618981]
Centroid: CG[39.46597609676; 25.67987206327]
Coordinates of the circumscribed circle: U[41.22883653274; 27.66884590705]
Coordinates of the inscribed circle: I[38.72883653274; 24.67326897998]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.1344339356° = 121°8'4″ = 1.02773995946 rad
∠ B' = β' = 115° = 1.13444640138 rad
∠ C' = γ' = 123.8665660644° = 123°51'56″ = 0.98797290452 rad

How did we calculate this triangle?

1. Use 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. 2. The triangle circumference is the sum of the lengths of its three sides 3. Semiperimeter of the triangle 4. The triangle area using Heron's formula 5. Calculate the heights of the triangle from its area. 6. Calculation of the inner angles of the triangle using a Law of Cosines     