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Date November 2016 Marks available 2 Reference code 16N.1.sl.TZ0.11
Level SL only Paper 1 Time zone TZ0
Command term Calculate Question number 11 Adapted from N/A

Question

AC is a vertical communications tower with its base at C.

The tower has an observation deck, D, three quarters of the way to the top of the tower, A.

N16/5/MATSD/SP1/ENG/TZ0/11

From a point B, on horizontal ground 250 m from C, the angle of elevation of D is 48°.

Calculate CD, the height of the observation deck above the ground.

[2]
a.

Calculate the angle of depression from A to B.

[4]
b.

Markscheme

\(\tan 48^\circ  = \frac{{{\text{CD}}}}{{250}}\)    (M1)

 

Note:     Award (M1) for correct substitution into the tangent ratio.

 

\(({\text{CD}} = ){\text{ }}278{\text{ }}({\text{m}}){\text{ }}(277.653 \ldots )\)    (A1)     (C2)

[2 marks]

a.

\(\tan {\text{ABC (or equivalent)}} = \frac{{\frac{4}{3} \times 277.653 \ldots }}{{250}}\)     (M1)(M1)(M1)

 

Note:     Award (M1) for \(\frac{4}{3}\) multiplying their part (a), (M1) for substitution into the tangent ratio, (M1) for correct substitution.

 

OR

\(90 - {\tan ^{ - 1}}\left( {\frac{{250}}{{\frac{4}{3} \times 277.653 \ldots }}} \right)\)    (M1)(M1)(M1)

 

Note:     Award (M1) for \(\frac{4}{3}\) multiplying their part (a), (M1) for substitution into the tangent ratio, (M1) for subtracting from 90 and for correct substitution.

 

\({\text{(angle of depression}} = {\text{) }}56.0^\circ {\text{ }}(55.9687 \ldots )\)    (A1)(ft)     (C4)

 

Note:     Follow through from part (a).

 

[4 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 5 - Geometry and trigonometry » 5.2
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