The Tangent Ratio

Programme Outline

Jamie is hoping to relax and top up his suntan until Katie points out that the tan in question is the tangent ratio! She goes on to explain some right-angled triangle terminology and introduces the tangent as the opposite over the adjacent. Jamie demonstrates how the tangent increases as the angle increases.

On most roller coasters, the first drop is the steepest. How steep is the first drop on the 'Ultimate' roller coaster at Lightwater Valley? Jamie uses the tangent ratio to work out the angle of the first drop, drawing similar triangles to get the measurements he needs.

The 'Angel of the North' sculpture stands impressively beside the A1 and is as high as four double-decker buses. Katie sets out to calculate exactly how high that is, with the aid of a clinometer and the tangent ratio.

In this week's 'Tick or Trash', the unusual orientation of the triangle in a typical exam-type question leads Katie to make a common mistake in her solution.

Jamie takes to the high seas in a bid to illustrate a context that's a textbook favourite. Katie is at the top of a lighthouse looking down towards Jamie, and the task is to work out how far his boat is from the rocks at the foot of the cliff. Katie needs to apply the tangent ratio to the problem quickly as Jamie is beginning to feel seasick!