In this section you will learn to recognize and solve applied problems using the skills from the previous section. The main areas of application that you will study here are surveying and navigation.
After completing this section you should be able to:
· Use measurement of angles to calculate the dimensions of large or distant objects
· Use compass bearings and known distances to determine other distances and locations
· Recognize and solve applied problems using these skills
1. Read section 5.7 of the text up to the end of Example 5. Be sure to note the use of any unfamiliar terms in the applied examples and compare their use in the problems with what you can find in a dictionary.
2. Read the following Study Notes and Discussion
3. Follow the instructions below regarding Further Practice.
This section is just an opportunity to practice the with the concepts introduced in the previous section. The only “new” concepts are some of the terms used in the applied fields of surveying and navigation. Figure 3 identifies the angle of elevation and angle of depression and Examples 3 and 4 show how they are used; and the use of compass bearings is explained in the preamble to Example 5. We shall postpone the discussion of harmonic motion and Example 6 until the next Module.
Trigonometry applies most directly in situations where we are given right angled triangles, which is the case with most of the examples in this section. But even if we are not given one of the sides of a right triangle we may be able to get enough information to solve our problem.
For example, one day our surveyor friend (with eye level 1.5m)first observed the top of a tree at an angle of elevation of , but as he walked towards it he was prevented from reaching it because it was on the other side of a raging river. The best he could do was observe that the angle of elevation was at a point 25m closer to the tree than where he first saw it. How high is this tree? Hint: look at Example 4 in the text.(see answer#1)
Check your understanding, and practice for speed, by working through some of the Exercises on pp446-452.
Do enough of the odd numbered questions of each type to convince yourself that you can get the right answers. (Note that, as usual, the answers are in the back of the text and complete worked solutions are in the student study guide - but try to avoid looking at answers or solutions until you have made your own best effort)
As a minimum, you should try ##7,15,17,29,33,47,57