Apps. and Interpretation for IBDP Maths Ebook 1 | Page 158

Your Practice Set – Applications and Interpretation for IBDP Mathematics
42
Paper 1 – Angles of Elevation and Depression
Example
In the figure, the angle of elevation of the top A of a building OA from a point B is 35 .
C is a point on BO such that AC � 96 m and BC � 64 m.
(a) Find the size of the angle ˆ BAC .
(b) Find the size of the angle ˆ OCA .
(c) Find the height of the building OA .
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Solution
(a)
(b)
(c)
sin BAC ˆ sin 35
�
64 96
(M1)(A1) for substitution
sin BAC ˆ � 0.38238429
BAC ˆ � 22.48144954
BAC ˆ � 22.5
A1 N3
OCA ˆ �35 � 22.48144954
(M1) for valid approach
OCA ˆ � 57.48144954
OCA ˆ � 57.5
A1 N2
sin 57.48144954
OA
�
96
(M1) for valid approach
OA � 80.94887442
OA � 80.9 m A1 N2
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