Miss Loi is in serious trouble.
Yesterday she and her sharp tongue had the audacity to question the spending prowess of a smirking young triad chief, sooOOoOo hurting and bruising his ego in the process.
So it was no coincidence this afternoon when a van pulled up suddenly in front of Miss Loi, the moment she stepped out of a shopping centre laden with shopping bags. A group of evil-looking men in shades and black suits quickly jumped out, bundled a startled Miss Loi into the van and zoomed off, crucially leaving behind the shopping items that she’d just gotten at a discount, to her dismay.
Hours later, she found herself gagged and tied up in an old disused oil rig in the middle of the South China Sea! Awaiting, as told by one of the evil-looking men in shades and black suit, her fate at the hands of the smirking young triad chief!
But in true Hong Kong drama fashion, she managed to somehow messaged her hero (played by Louis Koo (古天樂)) via her mobilephone (with her hands tied) before it was taken away. And now her hero is on the way to save her!
Unfortunately when Louis Koo reached his speedboat at the harbour, he realized that he’d forgotten to bring along his trigonometry textbook (香港版)!
The diagram represents a map showing a harbour H and three oil rigs, P, Q and R, where R is due East of H. HPQ is a straight line which lies on a bearing of 060o and angle HPR = 104o. It is given that HP = 59km, PR = 41km and RQ = 53km.
- The luxury yacht of the smirking young triad chief leaves Q at 0945. It sails directly to R, where it stays for 50 minutes for the chief to indulge in some unspeakable pleasures with some other unfortunate lady held there, before going to P, where Miss Loi is held. When moving, it may be assumed that it travels at a constant speed of 12km/h. At what time does it arrive at P?
- The speedboat, powered by Miss Loi’s hero, has to travel from H to R, as the direct route from H to P is too heavily guarded.
- Calculate the distance between H and R.
- He reckons that he should turn towards P when distance between the speedboat and the oil rig P is the shortest. Calculate this distance and state the point on HR where he should turn.
- Calculate the bearing of R from Q.
- An enemy helicopter, C, is hovering at a point vertically above P. The angle of depression of R from the helicopter is 35o. If there’s a dense layer of cloud at a height of 20km, can the helicopter see the speedboat approaching?
As Miss Loi is not really confident in Louis Koo’s mathematical ability, can someone please pass the following notes to him before he sets off, so that he can reach Miss Loi in time before she gets subjected to any ‘unspeakable pleasures’?
Sine Rule
Cosine Rule
a2 = b2+c2-2bc cosA
b2 = a2+c2-2ac cosB
c2 = a2+b2-2ab cosC
Area of triangle
=
bc sinA
=ab sinC
=ac sinB
Bearings
Angles of Elevation & Depression
NOTE: While the question may be similar, do not expect to see cute faces of Miss Loi and Louis Koo appearing in the diagram of your actual E-Maths paper. They are exclusive to 香港版 only.
