2026 May TZC P2 Q2

A ship is sailing directly toward a vertical cliff of height \(h\) metres.

When the ship is at point \(\mathrm{A}\), the angle of elevation to the top of the cliff is \(15^{\circ}\). After sailing a further \(70\) metres towards the cliff, the ship reaches point \(\mathrm{B}\), and the angle of elevation to the top of the cliff is \(40^{\circ}\).
Point \(\mathrm{C}\) is at the base of the cliff, and \(\mathrm{BC} = x\) metres.

1. Find an expression in terms of \(h\) and \(x\) for

   1. \( \tan{40^\circ}\);

   2. \( \tan{15^\circ}\).

      [2]

2. Hence, find the value of \(x\).

   [2]

3. Find the value of \(h\).

   [2]