## 44 - Angle of elevation of the rope tied to a rowboat on shore

Problem 44
A rowboat is pushed off from a beach at 8 ft/sec. A man on shore holds a rope, tied to the boat, at a height of 4 ft. Find how fast the angle of elevation of the rope is decreasing, after 1 sec.

## 40 - Base angle of a growing right triangle

Problem 40
The base of a right triangle grows 2 ft/sec, the altitude grows 4 ft/sec. If the base and altitude are originally 10 ft and 6 ft, respectively, find the time rate of change of the base angle, when the angle is 45°.

## Length of one side for maximum area of trapezoid (solution by Calculus)

Problem
BC of trapezoid ABCD is tangent at any point on circular arc DE whose center is O. Find the length of BC so that the area of ABCD is maximum.

Solution
As described by Alexander Bogomolny of cut-the-knot.org, for maximum area of trapezoid, the point of tangency should be at the midline of AB and DC, thus H is the midpoint of BC.

## 26-27 Horizontal rod entering into a room from a perpendicular corridor

Problem 26
A corridor 4 ft wide opens into a room 100 ft long and 32 ft wide, at the middle of one side. Find the length of the longest thin rod that can be carried horizontally into the room.

Problem 27
Solve Problem 26 if the room is 56 feet long.

## 24-25 Largest rectangle inscribed in a circular quadrant

Problem 24
Find the area of the largest rectangle that can be cut from a circular quadrant as in Fig. 76.

Problem 25
In Problem 24, draw the graph of A as a function of $\theta$. Indicating the portion of the curve that has a meaning.

## 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

Problem 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.