# Triangle calculator

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

### Right isosceles triangle.

Sides: a = 110   b = 77.78217459305   c = 77.78217459305

Area: T = 3025
Perimeter: p = 265.5633491861
Semiperimeter: s = 132.782174593

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 45° = 0.78553981634 rad
Angle ∠ C = γ = 45° = 0.78553981634 rad

Height: ha = 55
Height: hb = 77.78217459305
Height: hc = 77.78217459305

Median: ma = 55
Median: mb = 86.96326356546
Median: mc = 86.96326356546

Inradius: r = 22.78217459305
Circumradius: R = 55

Vertex coordinates: A[77.78217459305; 0] B[0; 0] C[77.78217459305; 77.78217459305]
Centroid: CG[51.8544497287; 25.92772486435]
Coordinates of the circumscribed circle: U[38.89108729653; 38.89108729653]
Coordinates of the inscribed circle: I[55; 22.78217459305]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 135° = 0.78553981634 rad
∠ C' = γ' = 135° = 0.78553981634 rad

# How did we calculate this triangle?

### 1. Input data entered: angle α, angle β and height ha. ### 2. From angle α and angle β we calculate angle γ: ### 3. From side c and angle α we calculate height hb: ### 4. Calculation of the third side a 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    