Page 194 - Mathematics_Form_Two

Trigonometry

Height of the mast, DC= is given by; Example 8�25
DB BC −
DB BC DC= − Petro starts from point P, travelling 19.8
km in the direction N 41º 22ʹW. How
= 180.08 m −140.04 m far has he travelled west and north,
= 40.04 m
Therefore, the height of the mast is respectively?
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Solution
Mathematics for Secondary Schools Example 8�24 The information is presented in the
40 m correct to 2 significant figures.

following figure.

A man who is 172 cm tall, notices that
his shadow measures 158 cm in length.
Find the angle of elevation of the sun.

Solution
Consider the following figure.

X

172 cm

i Let x and y be the distances in km due
Y Z
158 cm west and north of P, respectively.
From the figure, XZ represents the Using a right-angled triangle PRQ, It
height of a man, YZ represents the follows that
length of his shadow and θ is the angle x
of elevation of the sun. It follows that, sin 41º 22 ¢ = 19.8km

XZ
tan q = x =19.8 km ×sin 41°2 ′ 2
YZ = 13.09 km

172 cm
tan q =
158 cm Similarly, y

= 1.089 cos 41º 22 ¢ = 19.8km
1
−
θ = tan (1.089) y = 19.8 km × cos 41°22′
q =
47º 26¢ = 14.86 km
Therefore, the angle of elevation of the Therefore, Mr. Petro travelled 13.09 km
sun is 47º 26¢. west of P and 14.86 km north of P.

188
Student's Book Form Two

11/10/2024 20:14:18
MATHEMATIC F2 v5.indd 188
MATHEMATIC F2 v5.indd 188 11/10/2024 20:14:18