# Triangle calculator ASA

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

### Right scalene triangle.

Sides: a = 135.7155484032   b = 57.35658419531   c = 123

Area: T = 3527.384428011
Perimeter: p = 316.0711325985
Semiperimeter: s = 158.0365662993

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 65° = 1.13444640138 rad

Height: ha = 51.98220461941
Height: hb = 123
Height: hc = 57.35658419531

Median: ma = 67.85877420162
Median: mb = 126.2998943588
Median: mc = 84.09548429224

Inradius: r = 22.32201789603
Circumradius: R = 67.85877420162

Vertex coordinates: A[123; 0] B[0; 0] C[123; 57.35658419531]
Centroid: CG[82; 19.11986139844]
Coordinates of the circumscribed circle: U[61.5; 28.67879209765]
Coordinates of the inscribed circle: I[100.687982104; 22.32201789603]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 115° = 1.13444640138 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    