Page 188 - Mathematics_Form_Two

Trigonometry

(b)

y
24 cm
FOR ONLINE READING ONLY
78º
Mathematics for Secondary Schools Solution = sin37 Let AC be the length of the ladder and

(a) From the given figure, it implies that
x
be the distance along the horizontal

AB
32 cm
ground.
x =

32 cm sin37
7 m.
AC =
x = 19.2580 cm From the figure, AB 3 m= and
Therefore, x = 19.3 cm. BA 3.0 m 3
AB
3
(a) sin x = = = = = 0.4286= = 0.4286
7m
AC 7.0 7
AC
(b) From the given figure, it follows that 3
y x = sin − 1 

7
= cos 78° 
24 cm x = 25º 23′
y = 24 cm × cos 78° Therefore, the ladder makes an angle

y = 4.9898 cm of 25º 23′ with the wall.
Therefore, y = 4.99 cm. (b) cos 25 23 = CB

AC
CB
Example 8�20 =
7m
A ladder 7 m long leans against a vertical CB= 7m×cos25°2 ′ 3 = 6.3245m
wall so that the distance between the
foot of the ladder and the wall is 3 m. Therefore, the ladder reaches 6.32 m up
Find the following: the wall (3 significant figures).
(a) The angle which the ladder makes Exercise 8�5
with the wall. 1. Use a scientific calculator to find

(b) The height above the ground at the value in each of the following
which the upper end of the ladder trigonometric ratios correct to 4
touches the wall. significant figures.

(a) sin 56º (d) cos 64º 15′
Solution (b) tan 36º (e) sin 26º 11′
Consider the following figure. (c) cos 2º (f) tan 70º

182
Student's Book Form Two

11/10/2024 20:14:11
MATHEMATIC F2 v5.indd 182
MATHEMATIC F2 v5.indd 182 11/10/2024 20:14:11