Page 192 - Mathematics_Form_Two

Trigonometry

3. In the third scenario, observe an Example 8�21
object which is at a position which
you need to look upwards. For From the top of a tower, the angle of
instance, looking at the top of the depression of a point on the ground 10 m
building. away from the base of a tower is 60º.
How high is the tower?
4. Study and reflect on all three cases Solution
FOR ONLINE READING ONLY
Mathematics for Secondary Schools 5. Use the internet or other relevant
and discover features such as
angles formed, and possibilities of
Consider the following figure.
determining distances between the
observer and the objects without
measurements.

sources to study and justify your
observations and share your
findings through visual diagrams.

In Activity 8.5, it can be deduced that
observing an object below or above
the horizontal level, the line of sight
forms an angle below or above. An
angle formed between a horizontal Let A be the top point of the tower, C
level and a line of sight by observing be the point of observation and B be the
an object downward is called an angle base of the tower. Thus, tan60° = AB .
of depression. The angle formed by It follows that, 10 m
observing an object upwards is called an
angle of elevation. Figure 8.16 illustrates
the angles of depression and elevation.

Therefore, the height of the tower is
17.32 m.

Example 8�22

Figure 8�16: Angles of elevation and depression Two pegs, P and Q are on level ground.
In Figure 8.16, if B and C are objects to be Both pegs lie due west of a flag post.
The angle of elevation of the top of the
ˆ
observed, CAD is the angle of depression flag post from P is 45° and from Q is
ˆ
and BAD is the angle of elevation. The 60°. If P is 24 m from the foot of the
line AB and AC are lines of sights and the flag post, find PQ.
line AD represents the horizontal level.

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 186 11/10/2024 20:14:15