IB AA HL May 2026 P2 TZC Q2

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

When the ship is at point \(A\), 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 \(B\), and the angle of elevation to the top of the cliff is \(40^\circ\). Point \(C\) is at the base of the cliff, and \(BC=x\) metres.

1. Find an expression in terms of \(h\) and \(x\) for[2]
   1. \(\tan40^\circ\)
   2. \(\tan15^\circ\)
2. Hence, find the value of \(x\).[2]
3. Find the value of \(h\).[2]