# Trigonometric Functions

## 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

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

**Problem 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?

## 16 - Light placed above the center of circular area

**Problem 16**

A light is to be placed above the center of a circular area of radius a. What height gives the best illumination on a circular walk surrounding the area? (When light from a point source strikes a surface obliquely, the intensity of illumination is

where $\theta$ is the angle of incidence and $d$ the distance from the source.)

## 14-15 Ladder reaching the house from the ground outside the wall

**Problem 14**

A wall 10 ft high is 8 ft from the house. Find the length of the shortest ladder that will reach the house, when one end rests on the ground outside the wall.

## 13 - Sphere cut into a circular cone

**Problem 13**

A sphere is cut in the shape of a circular cone. How much of the material can be saved?

## 12 - Cone of maximum convex area inscribed in a sphere

**Problem 12**

Find the altitude of the circular cone of maximum convex surface inscribed a sphere of radius a.

## 11 - Triangular gutter of maximum carrying capacity

**Problem 11**

A gutter having a triangular cross-section is to be made by bending a strip of tin in the middle. Find the angle between the sides when the carrying capacity is to a maximum.

## 10 - Largest conical tent of given slant height

**Problem 10**

Find the largest conical tent that can be constructed having a given slant height.

## 03 - Heaviest cylinder that can be made from a shot

**Problem 3**

Find the weight of the heaviest circular cylinder can be cut from a 16-lb shot.