# Triangle calculator SAS

Please enter two sides of the triangle and the included angle
°

### Acute scalene triangle.

Sides: a = 516   b = 356   c = 505.3366060886

Area: T = 85159.98326743
Perimeter: p = 1377.336606089
Semiperimeter: s = 688.6688030443

Angle ∠ A = α = 71.21879023847° = 71°13'4″ = 1.2432986883 rad
Angle ∠ B = β = 40.78220976153° = 40°46'56″ = 0.71217818793 rad
Angle ∠ C = γ = 68° = 1.18768238914 rad

Height: ha = 330.0777452226
Height: hb = 478.4276868957
Height: hc = 337.043296711

Median: ma = 352.8266114702
Median: mb = 478.6711356168
Median: mc = 364.2188157691

Inradius: r = 123.6598974876
Circumradius: R = 272.5111249197

Vertex coordinates: A[505.3366060886; 0] B[0; 0] C[390.7154778735; 337.043296711]
Centroid: CG[298.6843613207; 112.3487655703]
Coordinates of the circumscribed circle: U[252.6688030443; 102.0854510729]
Coordinates of the inscribed circle: I[332.6688030443; 123.6598974876]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.7822097615° = 108°46'56″ = 1.2432986883 rad
∠ B' = β' = 139.2187902385° = 139°13'4″ = 0.71217818793 rad
∠ C' = γ' = 112° = 1.18768238914 rad

# How did we calculate this triangle?

### 1. 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. ### 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    