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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°.

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

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+114.2522×171.56×114.25cos70°     (A1)

SN=171 (m)     A1

 

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

 

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3 - Core: Circular functions and trigonometry » 3.7 » The cosine rule.

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