2017 Maths AS/A Levels
PROBLEM SOLVING
Using the compound angle formula you can find θ in terms of x :
2.5 0.5
−
tan β − tan a
8x
x
x=
.
=
θ tan ( β − a=
tan =
)
2
2.5
0.5
+
x
1 + tan β tan a 1 +
4
5
.
x x
The maximum value of θ occurs when tan θ =
8x
attains its maximum value. So you
4x2 + 5
8x
:
4x2 + 5
2
2
d  8 x  8 4 x + 5 − 64 x
40 − 32 x 2
=

 =
2
2
dx  4 x 2 + 5 
4x2 + 5
4x2 + 5
need to find the maximum value of
(
(
)
The maximum occurs when x 2 =
)
(
)
5
5
, that is when x =
, so you should stand
2
4
approximately 1.12metres from the picture.
Where would you need to stand if the height of this is picture was 1m?
Or where would you need to stand if the bottom of the picture was 1m above eye level?
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AE 05/04/2016
Version 1.0