55 - Greatest angle subtended by a picture

Problem 55
The lower edge of the picture is a ft, the upper edge is b ft, above the eye of an observer. At what horizontal distance should he stand, if the vertical angle subtended by the picture is to be greatest?

20-21 Width of the second corridor for a pole to pass horizontally

Problem 20
A pole 24 feet long is carried horizontally along a corridor 8 feet wide and into a second corridor at right angles to the first. How wide must the second corridor be?

Problem 21
Solve Problem 20 if the pole is of length $L$ and the first corridor is of width $C$.

19 Direction of the man to reach his destination as soon as possible

Route plan of a man on an island to a point on the straight shoreProblem 19
A man on an island a miles south of a straight beach wishes to reach a point on shore b miles east of his present position. If he can row r miles per hour and walk w miles per hour, in what direction should he row, to reach his destination as soon as possible? See Fig. 57.


17-18 A man in a motorboat needs to catch a bus

17-given-figure.jpgProblem 17
A man in a motorboat at A receives a message at noon, calling him to B. A bus making 40 miles per hour leaves C, bound for B, at 1:00 PM. If AC = 30 miles, what must be the speed of the boat, to enable the man to catch the bus?