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Mathematics: Running fixes
The sum of angles in a triangle is 180°
Draw a triangle ABC, then draw a line DAE parallel to line BC. Now, angles α and
β in the triangle equal angles DAB and EAC, respectively.
Therefore, the sum of angles in the triangle is 180° : a straight line.
“Doubling the angle” yields two equal angles

α = 30° , β = 60° thus γ = 30° 
So, α + δ + γ = 180°
α + 180  β + γ = 180°
2α = β
α + 180  2α + γ = 180°
180°  α + γ = 180°
α + γ = 0
γ = α
Two equal angles render an triangle isosceles
In the triangle on the right, α = γ and β = 2α.
By constructing the bisector h of angle β we create two little triangles in which x=y.
Therefore, d_{1}=d_{2}.
Next math chapter: Distance of horizon
Further reading:
Online navigation courses.
Flotilla sailing holidays.
RYA & ASA sailing schools in Greece.
Yacht charters guide.