# Triangle calculator

Please enter what you know about the triangle:
You have entered height ha, height hb and height hc.

### Right scalene Pythagorean triangle.

Sides: a = 165   b = 220   c = 275

Area: T = 18150
Perimeter: p = 660
Semiperimeter: s = 330

Angle ∠ A = α = 36.87698976458° = 36°52'12″ = 0.64435011088 rad
Angle ∠ B = β = 53.13301023542° = 53°7'48″ = 0.9277295218 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 220
Height: hb = 165
Height: hc = 132

Median: ma = 234.9660102996
Median: mb = 198.305532015
Median: mc = 137.5

Inradius: r = 55
Circumradius: R = 137.5

Vertex coordinates: A[275; 0] B[0; 0] C[99; 132]
Centroid: CG[124.6676666667; 44]
Coordinates of the circumscribed circle: U[137.5; 0]
Coordinates of the inscribed circle: I[110; 55]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.1330102354° = 143°7'48″ = 0.64435011088 rad
∠ B' = β' = 126.8769897646° = 126°52'12″ = 0.9277295218 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# How did we calculate this triangle?

### 1. Input data entered: height ha, height hb and height hc. ### 2. From height ha, height hb and height hc we calculate area T: ### 3. From area T and height ha we calculate side a: ### 4. From area T and height hb we calculate side b: ### 5. From area T and height hc we calculate side c: 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. ### 6. The triangle circumference is the sum of the lengths of its three sides ### 7. Semiperimeter of the triangle ### 8. The triangle area using Heron's formula ### 9. Calculate the heights of the triangle from its area. ### 10. Calculation of the inner angles of the triangle using a Law of Cosines    