Page 193 - Mathematics_Form_Two
P. 193
Trigonometry
It follows that,
Solution
Consider the following figure.
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Therefore, PQ 10.14 m.=
Example 8�23
A mobile phone mast is erected on a Mathematics for Secondary Schools
hilltop. The angle of elevation of the
base of the mast from a point on the
ground 200 m from the base of the hill
is 35°, while the angle of elevation from
Let AB be the height of the flag post. It the same point to the top of the mast is
42 .° Find the height of the mast.
implies that
Solution
AB
= tan 45° = 1 The given information is translated into
24m the following figure.
AB 24m 1= × B
= 24m
By using the triangle AQB, it follows D
that
AB = tan 60° = 3 C 200 m 42º 35º A
QB In ABC,∆ it implies that,
QB = 3 BC
AB
= 3
Thus, 24m 3 tan 42° = 200m
QB
BC = 200tan 42 m°
24m = 180.08 m
QB =
3 In ADC,∆ it implies that,
DC
tan35° =
200m
DB BC DC= DC = 200tan35 m°
−
= 8 3m = 140.04 m
187
Student's Book Form Two
11/10/2024 20:14:16
MATHEMATIC F2 v5.indd 187 11/10/2024 20:14:16
MATHEMATIC F2 v5.indd 187
