Triangle calculator

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

Acute scalene triangle.

Sides: a = 115.4770053838   b = 136.0621843504   c = 150

Area: T = 7500
Perimeter: p = 401.5321897342
Semiperimeter: s = 200.7665948671

Angle ∠ A = α = 47.30438285023° = 47°18'14″ = 0.82656075562 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 72.69661714977° = 72°41'46″ = 1.26987875462 rad

Height: ha = 129.9043810568
Height: hb = 110.2443986218
Height: hc = 100

Median: ma = 131.0466096071
Median: mb = 115.2765584372
Median: mc = 101.4799452578

Inradius: r = 37.35769325359
Circumradius: R = 78.55553419733

Vertex coordinates: A[150; 0] B[0; 0] C[57.7355026919; 100]
Centroid: CG[69.2455008973; 33.33333333333]
Coordinates of the circumscribed circle: U[75; 23.36553964774]
Coordinates of the inscribed circle: I[64.70441051671; 37.35769325359]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.6966171498° = 132°41'46″ = 0.82656075562 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 107.3043828502° = 107°18'14″ = 1.26987875462 rad

How did we calculate this triangle?

1. Input data entered: side c, angle β and height hc. 2. 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. 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     