# Triangle calculator ASA

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

### Right scalene triangle.

Sides: a = 529.4565621705   b = 869.7265965667   c = 690

Area: T = 182662.1899488
Perimeter: p = 2089.182158737
Semiperimeter: s = 1044.591079369

Angle ∠ A = α = 37.5° = 37°30' = 0.65444984695 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 52.5° = 52°30' = 0.91662978573 rad

Height: ha = 690
Height: hb = 420.0455386016
Height: hc = 529.4565621705

Median: ma = 739.0440468336
Median: mb = 434.8632982833
Median: mc = 631.9440072598

Inradius: r = 174.8654828019
Circumradius: R = 434.8632982833

Vertex coordinates: A[690; 0] B[0; 0] C[-0; 529.4565621705]
Centroid: CG[230; 176.4855207235]
Coordinates of the circumscribed circle: U[345; 264.7287810853]
Coordinates of the inscribed circle: I[174.8654828019; 174.8654828019]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.5° = 142°30' = 0.65444984695 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 127.5° = 127°30' = 0.91662978573 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    