17N.2.AHL.TZ0.H_5

pestleMathematicsAAHLPaper 217N· sl-3-3-applications-angles-of-elevation-and-depression-bearingssource ↗

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 ${\text{SXN}} =$ 70°.

N17/5/MATHL/HP2/ENG/TZ0/05

Find, to 3 significant figures, the distance between the two yachts.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

attempt to use tan, or sine rule, in triangle BXN or BXS (M1)

${\text{NX}} = 80\tan 55{\rm{^\circ }}\left( { = \frac{{80}}{{\tan 35{\rm{^\circ }}}} = 114.25} \right)$ (A1)

${\text{SX}} = 80\tan 65{\rm{^\circ }}\left( { = \frac{{80}}{{\tan 25{\rm{^\circ }}}} = 171.56} \right)$ (A1)

Attempt to use cosine rule M1

${\text{S}}{{\text{N}}^2} = {171.56^2} + {114.25^2} - 2 \times 171.56 \times 114.25\cos 70$ ° (A1)

${\text{SN}} = 171{\text{ }}({\text{m}})$ A1

Note: Award final A1 only if the correct answer has been given to 3 significant figures.

[6 marks]

Examiners’ report

[N/A]