Yachting and similar triangles

A yacht has two parallel masts which are both perpendicular to a level deck.  One mast is 12 m high, the other is 8 m.  Stays are rigged from the head if each mast to the foot of the other.  Find the perpendicular height of the crossing point above the deck.

SailBoat

Finding the height of the crossing point is a good similar triangles challenge for bright maths pupils.  In fact that the distance between the two masts is not given introduces two variables and makes this a subtle challenge.

160508SimilarSailboat

I find the independence of ‘h’ with the distance between the masts intriguing.

 

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