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Date November 2016 Marks available 4 Reference code 16N.1.SL.TZ0.T_11
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 0
Command term Calculate Question number T_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

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

tan 48 = CD 250    (M1)

 

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

 

( CD = )   278   ( m )   ( 277.653 )    (A1)     (C2)

[2 marks]

a.

tan ABC (or equivalent) = 4 3 × 277.653 250      (M1)(M1)(M1)

 

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

 

OR

90 tan 1 ( 250 4 3 × 277.653 )    (M1)(M1)(M1)

 

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

 

(angle of depression = 56.0   ( 55.9687 )    (A1)(ft)     (C4)

 

Note:     Follow through from part (a).

 

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 3— Geometry and trigonometry » SL 3.2—2d and 3d trig, sine rule, cosine rule, area
Show 133 related questions
Topic 3— Geometry and trigonometry » SL 3.3—Applications: angles of elevation and depression, bearings
Topic 3— Geometry and trigonometry

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