# Triangle calculator

Please enter what you know about the triangle:
You have entered area S and aspect ratio a:b:c = 9:15:16.

### Acute scalene triangle.

Sides: a = 25.86884030848   b = 43.11440051413   c = 45.98882721507

Area: T = 548
Perimeter: p = 114.9710680377
Semiperimeter: s = 57.48553401884

Angle ∠ A = α = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ B = β = 67.11546195238° = 67°6'53″ = 1.17113710869 rad
Angle ∠ C = γ = 79.32880707142° = 79°19'41″ = 1.38545360232 rad

Height: ha = 42.36882898557
Height: hb = 25.42109739134
Height: hc = 23.83221630438

Median: ma = 42.65664852962
Median: mb = 30.45223129984
Median: mc = 27.11657807353

Inradius: r = 9.53328652175
Circumradius: R = 23.39988509885

Vertex coordinates: A[45.98882721507; 0] B[0; 0] C[10.0659934533; 23.83221630438]
Centroid: CG[18.68327355612; 7.94440543479]
Coordinates of the circumscribed circle: U[22.99441360753; 4.33331205534]
Coordinates of the inscribed circle: I[14.37113350471; 9.53328652175]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ B' = β' = 112.8855380476° = 112°53'7″ = 1.17113710869 rad
∠ C' = γ' = 100.6721929286° = 100°40'19″ = 1.38545360232 rad

# How did we calculate this triangle?

### 1. Input data entered: area S and aspect ratio a:b:c. ### 2. From side a and angle β we calculate height hc: 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. ### 3. The triangle circumference is the sum of the lengths of its three sides ### 4. Semiperimeter of the triangle ### 5. The triangle area using Heron's formula ### 6. Calculate the heights of the triangle from its area. ### 7. Calculation of the inner angles of the triangle using a Law of Cosines    