Chapter 7: Small Angles & Approximation
Example 5
In triangle
ABC
, angle
B
is
p
/6 radians and angle
A
is almost a right angle, so that
Ð
A
= (
p
/2
-
x
) radians
, where
x
is small.
Show that
BC
¾¾
AC
»
2
-
x
2
.
Solution
Using sine rule,
BC
¾¾¾¾¾
sin (
p
/2
-
x
)
=
AC
¾¾¾
sin
p
/6
BC
¾¾
AC
=
sin (
p
/2
-
x
)
¾¾¾¾¾
sin
p
/6
=
cos
x
¾¾
½
»
2(1
-
½
x
2
)
»
2
-
x
2
Index
