Date | November 2017 | Marks available | 6 | Reference code | 17N.2.hl.TZ0.5 |
Level | HL only | Paper | 2 | Time zone | TZ0 |
Command term | Find | Question number | 5 | Adapted from | N/A |
Question
Barry is at the top of a cliff, standing 80 m above sea level, and observes two yachts in the sea.
“Seaview” (S) is at an angle of depression of 25°.
“Nauti Buoy” (N) is at an angle of depression of 35°.
The following three dimensional diagram shows Barry and the two yachts at S and N.
X lies at the foot of the cliff and angle SXN= 70°.
Find, to 3 significant figures, the distance between the two yachts.
Markscheme
attempt to use tan, or sine rule, in triangle BXN or BXS (M1)
NX=80tan55∘(=80tan35∘=114.25) (A1)
SX=80tan65∘(=80tan25∘=171.56) (A1)
Attempt to use cosine rule M1
SN2=171.562+114.252−2×171.56×114.25cos70° (A1)
SN=171 (m) A1
Note: Award final A1 only if the correct answer has been given to 3 significant figures.
[6 marks]