dy/dan: Marine Ramp

Trigonometry using ratios

This resource from the dy/dan collection features an animation showing a ramp that connects a boat dock to a floating platform. The height of the platform varies with the tide. Four options are given for a bridge that links the shore with the ramp. Which bridge is best?

Marine Ramp

A suitable starting point is to clarify what ‘best’ could mean.  Safety, usability and cost are all likely to be factors to consider. What additional information would be needed in order to use trigonometry? It is then revealed that the maximum desired angle is 18 degrees and that the dock drops below the pier by a maximum of 4.1 metres.

A sequel to the problem involves an interactive program where the maximum drop of the pier can be varied. This gives scope to work on a general solution to the problem.

A note on trigonometry

Trigonometric ratios can be a big conceptual jump for some students. The following diagrams link trigonometry with earlier work on ratio.

Trigonometry using ratios

Each of the smaller triangles is congruent and they are similar to the large triangle.

We have recently added the ‘dy/dan Three Act Math’ resources, this example being ‘Marine Ramp’.

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Encourage active learning in secondary mathematics lessons with the use of manipulatives.

Manipulatives - or “objects to think with - include counters, interlocking cubes, Cuisenaire rods and tiles etc". Research suggests that their use is beneficial to mathematical understanding, and can help students with retention, problem solving and reasoning.

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This is a residential course, fees include meals and accommodation for the duration of the course. 

A full list of CPD is available here.

 

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Subject(s)Mathematics
Age11-14, 14-16
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