College Algebra & Trigonometry, 2018a

8.4. APPLICATIONS 367
8.4 Applications
Trigonometry is often used for what is called “indirect measurement.” This is a
method of measuring inaccessible distances by using the relationships between
lengths and angles within a triangle. Two simple examples of this process are
measuring the height of a tall tree and measuring the distance across a body of
water. In both cases, while it might be possible to measure the distance directly,
it is often much easier to use indirect measurement.
In one example of indirect measurement, the angle of elevation of an object can
be used to create a right triangle in which one angle and one side are known.
The other sides of the triangle may then be solved for. In the problems in this
text, the angle of elevation will typically be given in the problem. In order to
actually measure the angle of elevation of an object, it is possible to use a simple
protractor.
If you wanted to measure the height of a tall tree that sits on flat ground, you
could use a specially modified protractor to do this. Modifying the protractor
by tying a weight to the end of a string and tying the other end of the string
through the hole in the protractor will help to measure the angle of elevation.
Once the protractor is ready, hold it upside down and sight the top of the tree
along the straight edge of the protractor. The weight hanging down will show
the complement to the angle of elevation. In other words, if the angle of elevation
is 20 ◦ , the string will mark out a measurement of 70 ◦ on the protractor.
70 ◦ 20 ◦