Page 195 - Mathematics_Form_Two

Trigonometry

Example 8�26 12.12
=
From point A, Fatuma observes the angle 0.2209
of elevation of the top of a church tower = 54.88
to be 32°. Moving 30m further away to Substituting the value of x in equation
point B on the same horizontal level as (i) gives,
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the bottom of the tower C, she observes h = 54.88 × tan 32°
the angle of elevation to be 22º. Find the = 54.88 × 0.6249
distance AC and the height of the tower. = 34.29

Solution Therefore, the distance AC is 54.88 m Mathematics for Secondary Schools
Present the information as shown in the and the height of the tower is 34.29 m.
following figure.

Exercise 8�6

1. A man whose eye is 180 cm above
the ground is standing 8 m from a
tree 7 m tall. What is the angle of
elevation of the top of the tree from
his eye?
Let h be the height of the tower and x be 2. The length of the shadow of a 16 m

the distance AC as shown in the figure. It tree is 8 m. What is the size of the

follows that, angle of elevation of the sun?
h h 3. Find the height of a tower if the
tan32º = and t n 22ºa =
x x + 3 0 angle of elevation of the top at a
Thus, h = x tan32 º (i) point 20 m from its foot is 34°.

Similarly, 4. A tree casts a 60 m shadow when the
o
h = (x + 30) tan 22° angle of elevation of the Sun is 25 .
h = x tan 22° + 30 tan 22° (ii) How tall is the tree?
Equating equations (i) and (ii) gives, 5. The angle of elevation of the top of
x tan 32º = tan 22º 30m tan 22ºx + 30 tan 22° a tree from a point on the ground 30
m from the base of the tree is 37°.
30m tan 22º
x (tan 32º tan 22º)- = 30 tan 22° Find the height of the tree.

30 tan 22°
30m tan 22º 6. From the top of a cliff 80 m high,
x =
tan 32º tan 22º- two boats are seen in a direction due
30 × 0.4040 west. Find the distance between the
= boats if their angles of depression
0.6249 – 0.4040

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Student's Book Form Two

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MATHEMATIC F2 v5.indd 189