| Date | May Specimen | Marks available | 4 | Reference code | SPM.1.sl.TZ0.2 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Calculate | Question number | 2 | Adapted from | N/A |
Question
Tom stands at the top, T , of a vertical cliff \(150{\text{ m}}\) high and sees a fishing boat, F , and a ship, S . B represents a point at the bottom of the cliff directly below T . The angle of depression of the ship is \({40^ \circ }\) and the angle of depression of the fishing boat is \({55^ \circ }\) .
Calculate, SB, the distance between the ship and the bottom of the cliff.
Calculate, SF, the distance between the ship and the fishing boat. Give your answer correct to the nearest metre.
Markscheme
\(150\tan 50\) (M1)
OR
\(\frac{{150}}{{\tan 40}}\) (M1)
\( = 179{\text{ (m)}}\) (\(178.763 \ldots \)) (A1) (C2)
\(150\tan 50 - 150\tan 35\) (M1)(M1)
Note: Award (M1) for \(150\tan 35\), (M1) for subtraction from their part (a).
\( = 73.7{\text{ (m)}}\) (\(73.7319 \ldots \)) (A1)(ft)
\( = 74{\text{ (m)}}\) (A1)(ft) (C4)
Note: The final (A1) is awarded for the correct rounding of their answer to (b).
Note: There will always be one answer with a specified degree of accuracy on each paper.
