The lower edge of a mural, which is 4 m high, is 2 m above an observers

Question:

The lower edge of a mural, which is 4 m high, is 2 m above an observer’s eye level, as shown in Figure 2.53. Show that the optical angle θ° is given by

cos 0 = 12 + d [(4 + d)(36 + d)]

where d m is the distance of the observer from the mural. See Review exercises Question 23.


Figure 2.53

90 dm 4 m 2 m


Data from  Review exercises Question 23

Continuing Question 54 of Exercises 2.6.2, show that

cot 0 = 12 + d 4d

and by applying the arithmetic–geometric inequality to

3 d + d 4

deduce that u° achieves its maximum value where d = 2√3.

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