# Triangle calculator

Please enter what you know about the triangle:
You have entered side c, angle α and angle β.

### Right scalene triangle.

Sides: a = 40.15503505446   b = 57.34106431002   c = 70

Area: T = 1151.123346046
Perimeter: p = 167.4910993645
Semiperimeter: s = 83.74554968224

Angle ∠ A = α = 35° = 0.61108652382 rad
Angle ∠ B = β = 55° = 0.96599310886 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 57.34106431002
Height: hb = 40.15503505446
Height: hc = 32.88992417275

Median: ma = 60.75332880868
Median: mb = 49.33659705148
Median: mc = 35

Inradius: r = 13.74554968224
Circumradius: R = 35

Vertex coordinates: A[70; 0] B[0; 0] C[23.02992949836; 32.88992417275]
Centroid: CG[31.01097649945; 10.96330805758]
Coordinates of the circumscribed circle: U[35; 0]
Coordinates of the inscribed circle: I[26.40548537222; 13.74554968224]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145° = 0.61108652382 rad
∠ B' = β' = 125° = 0.96599310886 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: side c, angle α and angle β. ### 2. From angle α and angle β we calculate angle γ: ### 3. From angle α, angle γ and side c we calculate side a - By using the law of sines, we calculate unknown side a: ### 4. Calculation of the third side b 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    