# Trigonometric Functions

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

## 45 - Angle of elevation of the the kite's cord

**Problem 45**

A kite is 60 ft high with 100 ft of cord out. If the kite is moving horizontally 4 mi/hr directly away from the boy flying it, find the rate of change of the angle of elevation of the cord.

## 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°.

## 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.

## 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.

## 23 - Sphere cut into a pyramid

**Problem 23**

A sphere is cut in the form of a right pyramid with a square base. How much of the material can be saved?

## 22 - Smallest cone that may circumscribe a sphere

**Problem 22**

A sphere of radius *a* is dropped into a conical vessel full of water. Find the altitude of the smallest cone that will permit the sphere to be entirely submerged.

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

**Problem 20**

A pole 27 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?